CN111723422A - Method, device and system for checking initial tension stage of stay cable of cable-stayed bridge - Google Patents
Method, device and system for checking initial tension stage of stay cable of cable-stayed bridge Download PDFInfo
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- CN111723422A CN111723422A CN202010503832.0A CN202010503832A CN111723422A CN 111723422 A CN111723422 A CN 111723422A CN 202010503832 A CN202010503832 A CN 202010503832A CN 111723422 A CN111723422 A CN 111723422A
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Abstract
The embodiment of the application provides a method, a device and a system for checking the initial tension stage of a stay cable of a cable-stayed bridge, wherein the checking method comprises the step of determining the initial tension theoretical pulling-out quantity of △ L of the kth stay cable according to a theoretical analysis modelTheory of k；△LTheory of kThe theoretical pulling amount of the kth stay cable in the theoretical analysis model from the unstressed length to the initial stretching in-place state is adopted, and the unstressed length is equal to the distance L between the tower end anchor point and the beam end anchor point before the installation of the kth stay cable in the theoretical analysis modelk theory 1Actually constructing the kth stay cable to obtain the initial tension actual pulling-out amount of the kth stay cable of △ Lk actual；△Lk actualThe actual length of the kth stay cable is stretched from the unstressed length to the initial stretching in place in the actual stretching processActual amount of extraction between according to △ Lk actualAnd △ LTheory of kAnd checking the physical parameters and the working state of the kth stay cable. The technical problem that the quality and the working state of a stay cable of a cable-stayed bridge cannot be found to be abnormal in time in the initial tensioning stage of the stay cable is solved.
Description
Technical Field
The application relates to the technical field of bridge engineering, in particular to a method, a device and a system for checking an initial tensioning stage of a stay cable of a cable-stayed bridge.
Background
The stay cable is an important structural member of the cable-stayed bridge, and the pulling-out amount of the stay cable refers to the length of a pulling end pulling-out part corresponding to the cable force change value in the tensioning process of the stay cable. The tension force and the pulling-out amount of the stay cable are important parameters for designing and constructing the cable-stayed bridge, and the verification of the tension force and the pulling-out amount is the key for controlling the quality and the stress state of the stay cable.
The cable-stayed bridge is generally formed by construction in stages, the construction of a stay cable is generally divided into a primary tensioning stage and a final tensioning stage, the primary tensioning stage corresponds to a construction intermediate state, and the final tensioning stage corresponds to a construction completion state. For final tension of the stay cable, the pull-out amount of the stay cable is generally controlled at present, and the cable force is used for checking. For the initial tension of the stay cable, at present, only the cable force control is adopted, and the pulling amount of the stay cable is not adopted for checking. The single control of the cable force adopted in the initial tensioning stage mainly has the following problems:
1. it is impossible to verify whether physical parameters (e.g., modulus of elasticity) of the stay cable satisfy the requirements;
2. the influence of an oil pressure gauge and other cable force testing equipment is large, the reliability of a cable force value is poor, and the precision is low;
3. the stay cable forms a two-point supporting state through the tower end anchor point and the beam end anchor point, and the cable force single control cannot verify whether the stay cable is in a normal supporting state.
In summary, the single control of the cable force in the initial tensioning stage is not favorable for finding the quality problems of the stay cable and the related equipment as soon as possible, and it is impossible to verify whether the stay cable is in a normal working state. Because the stay cable belongs to the customization product, if the cable-stay bridge construction later stage finds the problem, the rectification degree of difficulty is big, the time is long, will be in very passive situation.
Therefore, the single control of the cable force is adopted for the calibration of the initial tensioning stage of the stay cable of the cable-stayed bridge, so that the abnormity of the quality and the working state of the stay cable cannot be found in time, and the technical problem which needs to be solved by the technical personnel in the field is urgently needed.
The above information disclosed in the background section is only for enhancement of understanding of the background of the present application and therefore it may contain information that does not form the prior art that is known to those of ordinary skill in the art.
Disclosure of Invention
The embodiment of the application provides a method, a device and a system for checking a stay cable of a cable-stayed bridge in an initial tension stage, which are used for solving the technical problem that the stay cable cannot be found in time due to the fact that single control of cable force is adopted in the checking of the stay cable of the cable-stayed bridge in the initial tension stage.
The embodiment of the application provides a method for checking an initial tensioning stage of a stay cable of a pull bridge, which comprises the following steps:
determining the initial tension theoretical pulling-out amount △ L of the kth stay cable according to a preset theoretical analysis modelTheory of kWherein the initial stretching theoretical extraction amount is △ LTheory of kThe theoretical pulling amount of the kth stay cable in the theoretical analysis model from the unstressed length to the initial stretching in-place state is adopted, and the unstressed length is equal to the distance L between the tower end anchor point and the beam end anchor point before the installation of the kth stay cable in the theoretical analysis modelk theory 1K is an integer of 1 or more;
the k stay cable is actually constructed, and the initial tension actual pulling-out amount △ L of the k stay cable is obtainedk actualWherein the actual pulling amount of the initial tension is △ Lk actualThe actual pulling amount of the k-th stay cable in the actual stretching process is from the unstressed length to the initial stretching in-place state;
according to △ Lk actualAnd △ LTheory of kAnd checking the physical parameters and the working state of the kth stay cable.
The embodiment of the application also provides the following technical scheme:
the utility model provides a calibration equipment of cable-stay bridge suspension cable initial tension stage, includes:
a preliminary tension theoretical pulling-out amount determining module for determining △ L of the preliminary tension theoretical pulling-out amount of the kth stay cable according to a preset theoretical analysis modelTheory of kWherein the initial stretching theoretical extraction amount is △ LTheory of kThe theoretical pulling amount of the kth stay cable in the theoretical analysis model from the unstressed length to the initial stretching in-place state is adopted, and the unstressed length is equal to the distance L between the tower end anchor point and the beam end anchor point before the installation of the kth stay cable in the theoretical analysis modelk theory 1K is an integer of 1 or more;
an actual initial-tensioning pulling-out amount obtaining module, configured to perform actual construction on the kth stay cable, and obtain an actual initial-tensioning pulling-out amount △ L of the kth stay cablek actualWherein the actual pulling amount of the initial tension is △ Lk actualThe actual pulling amount of the k-th stay cable in the actual stretching process is from the unstressed length to the initial stretching in-place state;
a checking module for checking according to △ Lk actualAnd △ LTheory of kAnd checking the physical parameters and the working state of the kth stay cable.
The embodiment of the application also provides the following technical scheme:
the utility model provides a check-up system of cable-stay bridge suspension cable initial tension stage which characterized in that includes:
one or more processors;
storage means for storing one or more programs;
the one or more programs, when executed by the one or more processors, cause the one or more processors to implement a method of verifying an initial tension stage of a cable-stayed bridge cable as described above.
Due to the adoption of the technical scheme, the embodiment of the application has the following technical effects:
firstly, determining the initial tension theoretical pulling-out amount △ L of the kth stay cable according to a preset theoretical analysis modelTheory of kThe step has the functions of finding out the theoretical pulling amount between the unstressed length stretching state and the initial stretching in-place state, and actually constructing the kth stay cable to obtain the initial stretching actual pulling amount △ L of the kth stay cablek actualThe step is used for finding out the actual pulling amount of the stay cable from the unstressed length to the initial tensioning in-place state in the actual tensioning process, and finally comparing the actual pulling amount with the theoretical pulling amount if △ Lk actualAnd △ LTheory of kIf the deviation is large, the problem of the stay cable is shown, so that large deviation is caused, the deviation can be the problem of the physical parameters of the stay cable, the problem of a cable force testing device such as an oil pressure gauge can be caused, the problem of other devices related to the stay cable can be caused, the reasons can be checked, the abnormal problems of the quality and the working state of the stay cable of the cable-stayed bridge can be found and solved in the initial tensioning stage, if the stay cable and the cable force testing device are replaced, the situation that the problems can not be found or can be solved after the stay cable of the cable-stayed bridge is finally tensioned is avoided.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
fig. 1a is a schematic diagram of a mechanical displacement stage in an initial tension stage of a stay cable of a cable-stayed bridge;
fig. 1b is a schematic view of a sag resistance stage in an initial tension stage of a stay cable of a cable-stayed bridge;
fig. 1c is a schematic diagram of the elastic elongation stage in the initial tension stage of the stay cable of the cable-stayed bridge;
fig. 2 is a flowchart of a method for checking an initial tension stage of a stay cable of a cable-stayed bridge according to an embodiment of the present application;
FIG. 3 is a graph showing △ L for determining the initial pull-out amount of the kth stay cable in FIG. 2Theory of kA flow chart of (1);
FIG. 4 is a flowchart of step S110 in FIG. 2;
FIG. 5 is a flowchart of step S120 in FIG. 2;
FIG. 6 is a schematic view of the unstressed length of the stay cable of the verification method shown in FIG. 2;
fig. 7 is a schematic diagram of the external load on the stay cable in the coordinate system where the stay cable is located in the derivation of the unstressed length of the stay cable, which is a randomly distributed load in the X direction and the Y direction;
FIG. 8 is a schematic view of a cord micro-segment unit of any micro-segment dx on the cord of FIG. 7.
Description of reference numerals:
100 of the stay cables are arranged in the transverse direction,
anchor point at tower end 210 and anchor point at beam end 220.
Detailed Description
In order to make the technical solutions and advantages of the embodiments of the present application more apparent, the following further detailed description of the exemplary embodiments of the present application with reference to the accompanying drawings makes it clear that the described embodiments are only a part of the embodiments of the present application, and are not exhaustive of all embodiments. It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.
For clearly describing the method for checking the initial tension stage of the stay cable of the cable-stayed bridge in the embodiment of the present application, the starting point and the technical concept of the embodiment of the present application are explained first.
The starting point of the technical scheme of the embodiment of the application. At present, the pulling amount of the stay cable is not controlled in the initial tensioning stage of the stay cable, and the main reasons are that the stress state of the stay cable is complex in the initial tensioning stage, the theoretical calculation is difficult, and the actual pulling amount has many influence factors and is difficult to correspond to the theoretical value.
The pulling-out amount of the stay cable has the following characteristics: (1) the stay cable can generate certain sag under the action of self weight, and when the cable force is increased, the pulling-out amount of the stay cable comprises elastic extension caused by tension and extension caused by overcoming the sag; (2) the cable-stayed bridge is of a flexible system structure, and a tower end anchor point and a beam end anchor point can generate displacement in the process of tensioning the stay cable, so that the pulling-out amount of the stay cable is influenced; (3) the stay cable can generate certain bending torsion in a natural state, and the change value of the cable force and the cable length presents a strong nonlinear relation in a section with relatively small cable force. Therefore, the initial tension and pull-out amount of the stay cable is closely related to parameters such as the weight of the cable and the elastic modulus, as well as the cable force, the cable length, the cable sag, the structural system rigidity, and the like. The method is used for analyzing and monitoring the pulling-out amount of the stay cable, and is used for checking not only the physical parameters of the stay cable, but also the rigidity of a structural system.
Fig. 1 a-1 c are schematic diagrams of three stages of initial tension stage of a stay cable of a cable-stayed bridge, wherein a stay cable is represented by 100, a tower end anchor point is represented by 210, and a beam end anchor point is represented by 220. The initial tension process of the stay cable mainly comprises the following stages: (1) maneuver displacement phase (fig. 1 a). In the stage, the tension force of the stay cable is unchanged, the stay cable generates rigid body displacement under the action of the tension force, the pulling quantity of the stay cable is increased continuously, and the supporting state of the stay cable is gradually changed from multi-point elastic support to anchor point support at two ends; (2) sag resistant stage (fig. 1 b). In the stage, the tension of the stay cable is gradually increased, the pulling amount of the stay cable is continuously increased, and the pulling amount is mainly used for resisting the deformation generated by the sag; (3) elastic elongation phase (fig. 1 c). In the stage, the tension of the stay cable is further increased, the pulling amount of the stay cable is continuously increased, and the elastic elongation of the stay cable is mainly used in the pulling amount. The three stages are all divided according to ideal states, each state has an overlapping interval, and the pulling amount and the cable force change of the stay cable show obvious nonlinear characteristics.
According to the characteristics of the initial tension process of the stay cable, the amount of the stay cable pulled out from the tension position is related to not only the manufacturing state and the installation state of the stay cable but also various factors such as the type, the specification, the length and the inclination angle of the stay cable. Because the initial state of the stay cable cannot be predicted, the pulling amount generated by resisting the sag deformation is difficult to simulate, and the analysis of the pulling amount in the whole process of the initial tensioning of the stay cable is infeasible. Therefore, the pulling-out amount control of the stay cable initial tension needs to determine a specific section of the stay cable initial tension process, and the cable force and the pulling-out amount of the stay cable in the section can be judged through theoretical analysis and actual measurement.
The technical concept of the embodiment of the application is to find a mode of combining the cable force and the pulling amount of the stay cable to check the initial tensioning stage of the stay cable of the cable-stayed bridge.
The method for checking the initial tension stage of the stay cable of the cable-stayed bridge needs to calculate the initial tension pulling amount of the stay cable of the cable-stayed bridge, and the basic principle of the calculation is to determine the critical point of the sag resistance stage and the elastic elongation stage in the process of tensioning the stay cable, calculate the pulling amount of the stay cable from the critical point to the initial tension in place, and check the pulling amount with the corresponding cable force.
The method for calculating the pulling amount of the stay cable from the critical point to the initial tensioning position is based on the following basic assumption: (1) the stay cable can only be pulled and can not be pressed and bent; (2) the stay cable is made of linear elastic material, and the elastic extension of the stay cable accords with Hooke's law; (3) the pulling amount of the stay cable in the elastic elongation stage is only the elastic elongation value of the stay cable.
The method for calculating the pulling amount of the stay cable from the critical point to the initial tensioning position is based on the following definitions: (1) the initial stretching and drawing amount of the stay cable is the stretching and drawing amount of the stay cable in the elastic extension stage; (2) the stress-free installation state of the stay cable is taken as a critical point of a sag resisting stage and an elastic elongation stage, and the stress-free installation state is an ideal state that the stay cable is supposed not to be stressed and not to generate stress. After the stay cables are installed in the stress-free installation state, the stress-free length of the stay cables is equal to the distance L between the tower-end anchor point and the beam-end anchor point before the kth stay cable is installed in the theoretical analysis modelk theory 1. The cable force at the tensioning end of the stay cable in the unstressed installation state is the critical cable force.
Fig. 2 is a flowchart of a method for checking an initial tension stage of a stay cable of a cable-stayed bridge according to an embodiment of the present application.
As shown in fig. 2, the method for checking the initial tension stage of the stay cable of the cable-stayed bridge according to the embodiment of the present application includes the following steps:
step S100, determining the initial tension theoretical pulling-out quantity △ L of the kth stay cable according to a preset theoretical analysis modelTheory of kWherein the initial stretching theoretical extraction amount is △ LTheory of kThe theoretical pulling amount of the kth stay cable in the theoretical analysis model from the unstressed length to the initial stretching in-place state is adopted, and the unstressed length is equal to the distance L between the tower end anchor point and the beam end anchor point before the installation of the kth stay cable in the theoretical analysis modelk theory 1K is an integer of 1 or more;
step S200, the k-th stay cable is actually constructed, and the initial tension actual pulling-out amount △ L of the k-th stay cable is obtainedk actualWherein the actual pulling amount of the initial tension is △ Lk actualThe actual pulling amount of the k-th stay cable in the actual stretching process is from the unstressed length to the initial stretching in-place state;
step S300, according to △ Lk actualAnd △ LTheory of kAnd checking the physical parameters and the working state of the kth stay cable.
According to the method for checking the initial tensioning stage of the stay cable of the cable-stayed bridge, firstly, the initial tensioning theoretical pulling-out amount △ L of the kth stay cable is determined according to a preset theoretical analysis modelTheory of kThe step has the functions of finding out the theoretical pulling amount between the unstressed length stretching state and the initial stretching in-place state, and actually constructing the kth stay cable to obtain the initial stretching actual pulling amount △ L of the kth stay cablek actualThe step is used for finding out the actual pulling amount of the stay cable from the unstressed length to the initial tensioning in-place state in the actual tensioning process, and finally comparing the actual pulling amount with the theoretical pulling amount if △ Lk actualAnd △ LTheory of kIf the deviation is large, the problem occurs to the stay cable, which causes a large deviation, and the deviation may be the question of the physical parameters of the stay cableThe problems can be solved by finding and solving the problems of the stay cable of the cable-stayed bridge in the initial tensioning stage, such as replacing the stay cable, the cable force testing equipment and the like, so that the situation that the problems can not be found or can be solved after the stay cable of the cable-stayed bridge is tensioned finally is avoided.
When △ Lk actualRelative to △ LTheory of kWhen the error rate of (2) is less than or equal to any value within 5%, the physical properties and mechanical state of the stay cable are within a normal range.
In the implementation, fig. 3 shows that the initial tension theoretical pulling-out amount △ L of the kth stay cable is determined in fig. 2Theory of kIs described. As shown in fig. 3, step S100 specifically includes:
step S110: in a preset theoretical analysis model, determining the distance L between the anchor point at the tower end and the anchor point at the beam end before the inclined installation of the kth stay cablek theory 1；
Step S120: in a preset theoretical analysis model, when the kth stay cable is stretched to the initial stretching in-place state, determining the unstressed length L between anchor points when the kth stay cable is in the initial stretching in-place statek theory 2；
Step S130, calculating the initial tension theoretical pulling-out quantity △ L of the kth stay cableTheory of k，△LTheory of k＝Lk theory 1-Lk theory 2。
Respectively determine Lk theory 1And Lk theory 2Thereby calculating the initial tension theoretical pulling-out amount △ L of the kth stay cableTheory of k，△LTheory of k＝Lk theory 1-Lk theory 2。
In practice, fig. 4 is a flowchart of step S110 in fig. 2. As shown in fig. 4, step S110 specifically includes:
step S111: in a preset theoretical parting model, obtaining the deformed coordinate values of a tower end anchor point and a beam end anchor point when the stay cable is installed and is not subjected to initial tensioning according to the theoretical analysis result before the stay cable is subjected to initial tensioning;
step S112: in a preset theoretical parting model, calculating to obtain the distance L between a tower end anchor point and a beam end anchor point before the installation of the stay cable according to the deformed coordinate values of the tower end anchor point and the beam end anchor point when the stay cable is not initially tensioned during the installation of the stay cablek theory 1。
In a preset theoretical parting model, firstly, according to a theoretical analysis result before the stay cable is primarily tensioned, installing coordinate values of deformed tower end anchor points and beam end anchor points when the stay cable is not primarily tensioned; then calculate to obtain Lk theory 1. Thus, L can be conveniently calculatedk theory 1。
In practice, fig. 5 is a flowchart of step S120 in fig. 2. As shown in fig. 5, step S120 specifically includes:
step S121: in a preset theoretical analysis model, determining an initial tension theoretical value T required by the kth stay cable when the kth stay cable is tensioned to an initial tensioning in-place statek theory 2；
Step S122: in a preset theoretical analysis model, according to the initial tension theoretical value T required by the kth stay cablek theory 2Analyzing the construction stage, and simulating the unstressed length L between anchor points when the kth stay cable is in place in the initial tensioning state when the kth stay cable is tensioned to the initial tensioning statek theory 2。
Theoretical value T of initial tension required by kth stay cablek theory 2And the unstressed length L between anchor points when the kth stay cable is initially tensioned in placek theory 2The two values are the theoretical value T of the initial tension required by the kth stay cable in theoretical calculationk theory 2Can be calculated by theoretical analysis model. Therefore, in the above steps, the method firstly calculates T by theoretical calculationk theory 2Then through Tk theory 2And Lk theory 2The corresponding relation between the L and the L is calculated, so that the L can be conveniently obtainedk theory 2。
In the implementation, step S200 specifically includes:
step S210: when the k-th stay cable is actually constructed, the actual value F of the cable force of the k-th stay cablek actualIs Tk theory 1And Tk theory 2Respectively marking the pulling-out amount of the stay cable;
step S220, △ L is calculatedk actual，△Lk actualIs the length △ L between the marked pointsk actual。
Wherein, Tk theory 1And in a preset theoretical analysis model, when the length of the kth stay cable is the unstressed length, performing construction stage analysis, and simulating the cable force of the kth stay cable in the unstressed installation state.
The actual value F of the cable force of the k stay cable is adoptedk actualIs Tk theory 1And Tk theory 2△ L can be conveniently obtained by marking the pulling-out amount of the stay cablek actual。
In practice, step S200 further includes:
step S201: in the installation state model of simulating the full-bridge stay cable by using the cable unit, the kth stay cable is simulated and installed according to the unstressed length, the construction stage analysis is carried out, and the cable force T of the kth stay cable in the unstressed state is obtained through simulationk theory 1；
The preset theoretical analysis model comprises a model for simulating the installation state of the full-bridge stay cable by using a cable unit.
Thus, the k stay cable is installed according to the unstressed length simulation, the construction stage simulation is carried out, and the cable force T of the k stay cable in the unstressed installation state can be conveniently obtainedk theory 1。Tk theory 1And the stress-free length, wherein the theoretical calculation is based on the fact that the stress-free length is equal to the distance L between the anchor point at the tower end and the anchor point at the beam end before the k stay cable is installed in the theoretical analysis modelk theory 1，Lk theory 1Can be calculated by theoretical analysis model. Therefore, in the above steps, firstly calculating L by theoretical calculationk theory 1So that the stress-free length of the kth stay cable is equal to Lk theory 1Then, the construction stage analysis is carried out, and the obtained T is simulatedk theory 1。
In practice, step S200 further includes:
step S202: in a cantilever assembling construction stage model of a main beam of a cable-stayed bridge, each main beam segment of the cable-stayed bridge is installed corresponding to a pair of stay cables, and the simulation is carried out in stages according to the installation of the main beam, the installation of the stay cables and the initial tensioning of the stay cables in place; determining the initial tension theoretical value of each stay cable by taking the closure of the main beam sections as a target;
and the preset theoretical analysis model comprises a model of the construction stage of assembling the main girder cantilever of the cable-stayed bridge.
Establishing a model of a construction stage of assembling a main girder cantilever of a cable-stayed bridge, providing a precondition for determining an initial tension theoretical value of each stay cable, and calculating a distance L between a tower-end anchor point and a beam-end anchor point before installation of the stay cablek theory 1Preconditions are provided.
Specifically, a model of a main beam cantilever assembling construction stage of the cable-stayed bridge is established by adopting professional finite element software of the cable-stayed bridge, beams and towers are simulated by adopting beam units, stay cables are simulated by adopting cable units, and geometric nonlinearity is considered in the overall analysis.
Namely, geometric nonlinear factors such as a large displacement effect of a structure, a sag effect of a stay cable, a P-delta effect of a beam and a tower and the like need to be considered in a model in a main girder cantilever assembling construction stage of the cable-stayed bridge, and the construction stages before and after the stay cable is installed need to be considered in the model.
Specifically, in a model for simulating the installation state of the full-bridge stay cable by using the cable unit, the step of simulating and installing the kth stay cable according to the unstressed length specifically comprises the following steps:
the k stay cable reaches the unstressed length by adopting a cable force iteration mode;
or by using a finite element program with a stress-free length control function.
The two methods can realize the simulation and installation of the kth stay cable according to the unstressed length, and the k stay cable can be selected according to the actual condition.
Specifically, in a preset theoretical analysis model, according to the initial tension theoretical value T required by the kth stay cablek theory 2Simulating installation, analyzing construction stage, simulating unstressed length L between anchor points when the kth stay cable is in place in initial tension when the kth stay cable is stretched to the in-place state in initial tensionk theory 2The method specifically comprises the following steps:
the k-th stay cable reaches the required initial tension theoretical value T by adopting a cable force iteration modek theory 2；
Or a finite element program with a cable force control function is adopted.
Both methods can realize that the kth stay cable reaches the required initial tension theoretical value Tk theory 2The selection is performed according to actual conditions.
Specifically, fig. 6 is a schematic view of the unstressed length of the stay cable in the verification method shown in fig. 2. The unstressed length is calculated by the following formula:
wherein L is0The length of the stay cable is unstressed, l is the horizontal distance between a tower-end anchor point and a beam-end anchor point, H is the horizontal tension of the stay cable, EA is the elastic modulus of the stay cable with the cross-sectional area A, x is the horizontal coordinate of any point on the stay cable, y is the vertical coordinate of any point on the stay cable, q is the vertically uniform load along the length direction of the stay cable, H is the vertical distance between the tower-end anchor point and the beam-end anchor point, sinh is a hyperbolic sine function, and cosh is a hyperbolic cosine function.
Fig. 6 shows any stressed state of the stay cable under the two-point supporting condition, i.e. any state in two stages of fig. 1b and 1c, not the stage of fig. 1 a.
The calculation formula of the unstressed length is a basic equilibrium differential equation based on any tiny segment of the stay cable:
the basic Soxhlet equation is obtained by considering the boundary conditions as follows:
and respectively obtaining the total length (the length after elongation after stress) and the elongation of the stay cable by integration, and then subtracting the elongation from the total length to obtain the unstressed length of the stay cable. Total length and elongation respectively correspond to L0A first term and a second term in the formula.
The meaning of each parameter in the formula is:
L0the unstressed length of the stay cable is adopted;
h is the horizontal tension of the stay cable, and the horizontal tension of two anchor points of the stay cable is the same, namely H is HA is HB;
e is the elastic modulus of the stay cable;
a is the cross-sectional area of the stay cable; EA is the elastic modulus of the stay cable with the cross-sectional area of A;
q is a load which is vertically and uniformly distributed along the length direction of the stay cable, namely the self weight of the stay cable;
alpha A is an included angle between the tangent line of the anchor point (anchor point A) at the beam end of the stay cable and the X axis;
alpha B is an included angle between the tangent of an anchor point (anchor point B) at the tower end of the stay cable and the X axis;
l is the horizontal distance between the tower end anchor point (anchor point B) and the beam end anchor point (anchor point A);
h is the vertical distance between a tower-end anchor point (anchor point B) and a beam-end anchor point (anchor point A);
TA is the stay cable force at the anchor point (anchor point A) of the beam end;
TB is the stay cable force at the anchor point (anchor point B) at the tower end;
HA is the horizontal component of the stay cable force at the anchor point (anchor point A) of the beam end;
VA is the vertical component of the stay cable force at the anchor point (anchor point A) of the beam end;
HB is the horizontal component of the stay cable force at the anchor point (anchor point A) of the beam end;
VB is the vertical component force of the stay cable force at the anchor point (anchor point B) at the tower end.
The derivation basis and the process of the unstressed length of the stay cable are as follows:
first, basic premise
1. The cord is ideally flexible, neither stressed nor resistant to bending.
The size of the cross section of the cable is very small compared with the length of the cable, namely the bending rigidity of the cross section of the cable is not counted; the curve of the cable has a turning part, and when the turning curvature is not large, the local bending stress can be ignored.
2. The material of the cord complies with Hooke's law.
The deformation of the cable can be large, but the stress is small compared with the limit bearing capacity, and the cable is in the elastic range; the cable has inelastic deformation in the initial state, and the inelastic deformation can be eliminated by performing pretensioning.
Equation of equilibrium of two, one
Assuming that the cable is in the coordinate system as shown in fig. 7, the external loads on the cable are arbitrarily distributed loads in the X direction and the Y direction. According to the first precondition of the above paragraph, the tension of the cable can only act in the tangential direction of the cable.
Taking any micro-segment dx on the cord, the force applied to the cord micro-segment is shown in fig. 8.
From the static equilibrium conditions of the rope micro-segment unit, it can be obtained:
(1) equations (2) and (2) are the static equilibrium equations for the cables.
Considering that normally the ropes are only loaded by vertical dead weight and not horizontally, i.e. qx0, according to formula (1), in which case
Substituting the equation into the formula (2) to obtain the basic equilibrium equation of the cable under the general condition:
third, stay cable unstressed cable long solution and iterative algorithm
A computational diagram of a stay cable can generally be represented in the form shown in fig. 6.
Q in the formula (3)yThe load is vertically distributed along the X direction of the cable, the self weight q of the actual cable is vertically and uniformly distributed along the length direction of the cable, and the relationship between the load and the load is as follows:
qydx＝qds，
thus is provided with
By substituting formula (4) for formula (3), it is possible to obtain:
by integrating equation (5) and considering the boundary conditions x-0, y-0, and x-l, y-h, we can obtain
Wherein the content of the first and second substances,
deriving x from the left and right sides of formula (6) under boundary condition y'x＝0＝tanαBCan obtain
The length of the catenary wire of the cable obtained by the integration of the formula (6) is
The elastic elongation value of the cable caused by the tension T is
Wherein w is shown in formula (I).
The unstressed length of the cable being
S0＝S-ΔS(10)
Unstressed length L of cable0Using S in the derivation of the above formula0Is shown in the drawings.
Iterative algorithm of cable length (only representing one algorithm, and other methods can be adopted to solve the formula)
(1) Take initial value αB0＝atan(h/l)；
(2) Get HB0＝TBcosαB0；
(3) H is to beB0Substitution of formula (7) to αB1；
(4) Repeating the first three steps (α)B0→αB1) The process is carried out for 3 to 5 times to obtain stable HB；
(5) H is to beBAnd each parameter is substituted for formula (I), (8), (9) and (10) to obtain S, delta S, S0。
Example two
The second calibration equipment of this application embodiment's stay cable preliminary tension stage includes:
a preliminary tension theoretical pulling-out amount determining module for determining △ L of the preliminary tension theoretical pulling-out amount of the kth stay cable according to a preset theoretical analysis modelTheory of kWherein the initial stretching theoretical extraction amount is △ LTheory of kThe theoretical pulling amount of the kth stay cable in the theoretical analysis model from the unstressed length to the initial stretching in-place state is adopted, and the unstressed length is equal to the distance L between the tower end anchor point and the beam end anchor point before the installation of the kth stay cable in the theoretical analysis modelk theory 1K is an integer of 1 or more;
an actual initial-tensioning pulling-out amount obtaining module, configured to perform actual construction on the kth stay cable, and obtain an actual initial-tensioning pulling-out amount △ L of the kth stay cablek actualWherein the actual pulling amount of the initial tension is △ Lk actualThe actual pulling amount of the k-th stay cable in the actual stretching process is from the unstressed length to the initial stretching in-place state;
a checking module for checking according to △ Lk actualAnd △ LTheory of kAnd checking the physical parameters and the working state of the kth stay cable.
In an implementation, the initial tension theoretical pulling-out amount determining module includes:
Lk theory 1A determining submodule for determining the distance L between the tower end anchor point and the beam end anchor point before the k-th inclined stay cable is obliquely installed in a preset theoretical analysis modelk theory 1；
Lk theory 2A determining submodule for determining the unstressed length L between anchor points when the kth stay cable is in place in the initial tension state when the kth stay cable is in place in the preset theoretical analysis modelk theory 2；
△LTheory of kA calculation submodule for calculating the initial tension theoretical pulling-out amount △ L of the kth stay cableTheory of k，△LTheory of k＝Lk theory 1-Lk theory 2。
In practice, the Lk theory 1The determining of the sub-modules specifically comprises:
the two-end anchor point determining unit is used for acquiring deformed coordinate values of a tower-end anchor point and a beam-end anchor point when the stay cable is installed and is not subjected to primary tensioning according to a theoretical analysis result before the stay cable is subjected to primary tensioning in a preset theoretical parting model;
Lk theory 1A determining unit, configured to calculate, in a preset theoretical parting model, a distance L between a tower-end anchor point and a beam-end anchor point before installation of the stay cable according to coordinate values after deformation of the tower-end anchor point and the beam-end anchor point when the stay cable is not initially tensioned during installation of the stay cablek theory 1
In practice, theLk theory 2The determination submodule includes:
Tk theory 2A determining unit, configured to determine, in a preset theoretical analysis model, a theoretical initial tension value T required by the kth stay cable when the kth stay cable is tensioned to an initial tensioned statek theory 2；
Lk theory 2A determining unit for determining the theoretical value T of the initial tension required by the kth stay cable in a preset theoretical analysis modelk theory 2Analyzing the construction stage, and simulating the unstressed length L between anchor points when the kth stay cable is in place in the initial tensioning state when the kth stay cable is tensioned to the initial tensioning statek theory 2。
In the implementation, the initial tension actual pulling-out amount obtaining module comprises:
a marking submodule for marking the actual value F of the cable force of the kth stay cable when the kth stay cable is actually constructedk actualIs Tk theory 1And Tk theory 2Respectively marking the pulling-out amount of the stay cable;
△Lk actualA calculation submodule for calculating △ Lk actual，△Lk actualIs the length △ L between the marked pointsk actual；
Wherein, Tk theory 1And in a preset theoretical analysis model, when the length of the kth stay cable is the unstressed length, performing construction stage analysis, and simulating the cable force of the kth stay cable in the unstressed installation state.
In the implementation, the initial tension actual pulling-out amount obtaining module further comprises:
Tk theory 1The determining submodule is used for simulating and installing the kth stay cable according to the unstressed length in an installation state model of the full-bridge stay cable simulated by the cable unit, carrying out construction stage analysis and simulating to obtain the cable force T of the kth stay cable in an unstressed statek theory 1；
The preset theoretical analysis model comprises a model for simulating the installation state of the full-bridge stay cable by using a cable unit.
In the implementation, the initial tension actual pulling-out amount obtaining module further comprises:
Tk theory 2The determining submodule is used for installing each main beam segment of the cable-stayed bridge corresponding to a pair of stay cables in a cantilever assembling construction stage model of the main beam of the cable-stayed bridge, and simulating in stages according to main beam installation, stay cable installation and initial tensioning of the stay cables in place; determining the initial tension theoretical value of each stay cable by taking the closure of the main beam sections as a target;
and the preset theoretical analysis model comprises a model of the construction stage of assembling the main girder cantilever of the cable-stayed bridge.
EXAMPLE III
The utility model provides a check-up system in cable-stay bridge suspension cable initial tension stage of embodiment includes:
one or more processors;
storage means for storing one or more programs;
when executed by the one or more processors, the one or more programs cause the one or more processors to implement the method for verifying the initial tension stage of the cable-stayed bridge cable according to embodiment one.
In the description of the present application and the embodiments thereof, it is to be understood that the terms "top", "bottom", "height", and the like, indicate orientations or positional relationships based on those shown in the drawings, are merely for convenience in describing the present application and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and thus, should not be construed as limiting the present application.
In this application and its embodiments, unless expressly stated or limited otherwise, the terms "disposed," "mounted," "connected," "secured," and the like are to be construed broadly, e.g., as meaning fixedly connected, detachably connected, or integral to; the connection can be mechanical connection, electrical connection or communication; either directly or indirectly through intervening media, either internally or in any other relationship. The specific meaning of the above terms in the present application can be understood by those of ordinary skill in the art as appropriate.
In this application and its embodiments, unless expressly stated or limited otherwise, the first feature "on" or "under" the second feature may comprise the first and second features being in direct contact, or may comprise the first and second features being in contact, not directly, but via another feature in between. Also, the first feature being "on," "above" and "over" the second feature includes the first feature being directly on and obliquely above the second feature, or merely indicating that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature includes the first feature being directly above and obliquely above the second feature, or simply meaning that the first feature is at a lesser level than the second feature.
The above disclosure provides many different embodiments or examples for implementing different structures of the application. The components and arrangements of specific examples are described above to simplify the present disclosure. Of course, they are merely examples and are not intended to limit the present application. Moreover, the present application may repeat reference numerals and/or letters in the various examples, such repetition is for the purpose of simplicity and clarity and does not in itself dictate a relationship between the various embodiments and/or configurations discussed. In addition, examples of various specific processes and materials are provided herein, but one of ordinary skill in the art may recognize applications of other processes and/or use of other materials.
While the preferred embodiments of the present application have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all alterations and modifications as fall within the scope of the application.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present application without departing from the spirit and scope of the application. Thus, if such modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is intended to include such modifications and variations as well.
Claims (18)
1. A method for checking an initial tension stage of a stay cable of a cable-stayed bridge is characterized by comprising the following steps:
determining the initial tension theoretical pulling-out amount △ L of the kth stay cable according to a preset theoretical analysis modelTheory of kWherein the initial stretching theoretical extraction amount is △ LTheory of kThe theoretical pulling amount of the kth stay cable in the theoretical analysis model from the unstressed length to the initial stretching in-place state is adopted, and the unstressed length is equal to the distance L between the tower end anchor point and the beam end anchor point before the installation of the kth stay cable in the theoretical analysis modelk theory 1K is an integer of 1 or more;
the k stay cable is actually constructed, and the initial tension actual pulling-out amount △ L of the k stay cable is obtainedk actualWherein the actual pulling amount of the initial tension is △ Lk actualThe actual pulling amount of the k-th stay cable in the actual stretching process is from the unstressed length to the initial stretching in-place state;
according to △ Lk actualAnd △ LTheory of kAnd checking the physical parameters and the working state of the kth stay cable.
2. The verification method according to claim 1, wherein the theoretical initial tension pull-out amount △ L of the kth stay cable is determined according to a preset theoretical analysis modelTheory of kThe method specifically comprises the following steps:
in a preset theoretical analysis model, determining the distance L between the anchor point at the tower end and the anchor point at the beam end before the inclined installation of the kth stay cablek theory 1；
In a preset theoretical analysis model, when the kth stay cable is stretched to the initial stretching in-place state, determining the unstressed length L between anchor points when the kth stay cable is in the initial stretching in-place statek theory 2；
Calculating the initial tension theoretical pulling-out amount △ L of the kth stay cableTheory of k，△LTheory of k＝Lk theory 1-Lk theory 2。
3. The verification method according to claim 2, wherein a distance L between the tower-end anchor point and the beam-end anchor point before the k-th stay cable is obliquely installed is determinedk theory 1The method specifically comprises the following steps:
in a preset theoretical parting model, obtaining the deformed coordinate values of a tower end anchor point and a beam end anchor point when the stay cable is installed and is not subjected to initial tensioning according to the theoretical analysis result before the stay cable is subjected to initial tensioning;
in a preset theoretical parting model, calculating to obtain the distance L between a tower end anchor point and a beam end anchor point before the installation of the stay cable according to the deformed coordinate values of the tower end anchor point and the beam end anchor point when the stay cable is not initially tensioned during the installation of the stay cablek theory 1。
4. The verification method according to claim 3, wherein in the preset theoretical analysis model, when the kth stay cable is determined to be tensioned to the initial tensioning in-place state, the unstressed length L between anchor points of the kth stay cable is determined when the kth stay cable is initially tensioned in-placek theory 2The method specifically comprises the following steps:
in a preset theoretical analysis model, determining an initial tension theoretical value T required by the kth stay cable when the kth stay cable is tensioned to an initial tensioning in-place statek theory 2；
In a preset theoretical analysis model, according to the initial tension theoretical value T required by the kth stay cablek theory 2Analyzing the construction stage, and simulating the unstressed length L between anchor points when the kth stay cable is in place in the initial tensioning state when the kth stay cable is tensioned to the initial tensioning statek theory 2。
5. The verification method according to claim 4, wherein the k-th stay cable is actually constructed to obtain an initial tension actual pulling amount △ L of the k-th stay cablek actualThe method specifically comprises the following steps:
when the k-th stay cable is actually constructed, the actual value F of the cable force of the k-th stay cablek actualIs Tk theory 1And Tk theory 2Respectively marking the pulling-out amount of the stay cable;
calculate △ Lk actual，△Lk actualIs the length △ L between the marked pointsk actual；
Wherein, Tk theory 1And in a preset theoretical analysis model, when the length of the kth stay cable is the unstressed length, performing construction stage analysis, and simulating the cable force of the kth stay cable in the unstressed installation state.
6. The verification method according to claim 5, wherein the k-th stay cable is actually constructed to obtain an initial tension actual pulling amount △ L of the k-th stay cablek actualFurther comprising the steps of:
in the installation state model of simulating the full-bridge stay cable by using the cable unit, the kth stay cable is simulated and installed according to the unstressed length, the construction stage analysis is carried out, and the cable force T of the kth stay cable in the unstressed state is obtained through simulationk theory 1；
The preset theoretical analysis model comprises a model for simulating the installation state of the full-bridge stay cable by using a cable unit.
7. The verification method according to claim 6, wherein the k-th stay cable is actually constructed to obtain an initial tension actual pulling amount △ L of the k-th stay cablek actualFurther comprising the steps of:
in a cantilever assembling construction stage model of a main beam of a cable-stayed bridge, each main beam segment of the cable-stayed bridge is installed corresponding to a pair of stay cables, and the simulation is carried out in stages according to the installation of the main beam, the installation of the stay cables and the initial tensioning of the stay cables in place; determining the initial tension theoretical value of each stay cable by taking the closure of the main beam sections as a target;
and the preset theoretical analysis model comprises a model of the construction stage of assembling the main girder cantilever of the cable-stayed bridge.
8. The checking method according to claim 7, wherein the model of the construction stage of assembling the main girder cantilever of the cable-stayed bridge is established by using professional finite element software of the cable-stayed bridge, the girder and the tower are simulated by using the girder unit, the stay cable is simulated by using the cable unit, and the geometric nonlinearity is considered in the overall analysis.
9. The calibration method according to claim 8, wherein the step of simulating installation of the kth stay cable according to the unstressed length in the model of the installation state of the full-bridge stay cable by the cable unit comprises:
the k stay cable reaches the unstressed length by adopting a cable force iteration mode;
or a finite element program with a stress-free length control function is adopted for realization;
in a preset theoretical analysis model, according to the initial tension theoretical value T required by the kth stay cablek theory 2Simulating installation, analyzing construction stage, simulating unstressed length L between anchor points when the kth stay cable is in place in initial tension when the kth stay cable is stretched to the in-place state in initial tensionk theory 2The method specifically comprises the following steps:
the k-th stay cable reaches the required initial tension theoretical value T by adopting a cable force iteration modek theory 2；
Or a finite element program with a cable force control function is adopted.
10. A verification method according to claim 9, characterized in that the unstressed length is calculated by the following formula:
wherein L is0For unstressed length, l being tower-end anchor point and beam-endThe horizontal distance between anchor points, H is the horizontal tension of the stay cable, EA is the elastic modulus of the stay cable with the cross-sectional area of A, x is the horizontal coordinate of any point on the stay cable, y is the vertical coordinate of any point on the stay cable, q is the vertical uniform load along the length direction of the stay cable, and H is the vertical distance between the tower end anchor point and the beam end anchor point.
11. The utility model provides a calibration equipment of cable-stay bridge suspension cable initial tension stage which characterized in that includes:
a preliminary tension theoretical pulling-out amount determining module for determining △ L of the preliminary tension theoretical pulling-out amount of the kth stay cable according to a preset theoretical analysis modelTheory of kWherein the initial stretching theoretical extraction amount is △ LTheory of kThe theoretical pulling amount of the kth stay cable in the theoretical analysis model from the unstressed length to the initial stretching in-place state is adopted, and the unstressed length is equal to the distance L between the tower end anchor point and the beam end anchor point before the installation of the kth stay cable in the theoretical analysis modelk theory 1K is an integer of 1 or more;
an actual initial-tensioning pulling-out amount obtaining module, configured to perform actual construction on the kth stay cable, and obtain an actual initial-tensioning pulling-out amount △ L of the kth stay cablek actualWherein the actual pulling amount of the initial tension is △ Lk actualThe actual pulling amount of the k-th stay cable in the actual stretching process is from the unstressed length to the initial stretching in-place state;
a checking module for checking according to △ Lk actualAnd △ LTheory of kAnd checking the physical parameters and the working state of the kth stay cable.
12. The verification device of claim 11, wherein the initial tension theoretical pull-out determination module comprises:
Lk theory 1A determining submodule for determining the distance L between the tower end anchor point and the beam end anchor point before the k-th inclined stay cable is obliquely installed in a preset theoretical analysis modelk theory 1；
Lk theory 2A determination submodule for determiningIn a preset theoretical analysis model, when the kth stay cable is stretched to the initial stretching in-place state, the unstressed length L between anchor points of the kth stay cable in the initial stretching in-place state is determinedk theory 2；
△LTheory of kA calculation submodule for calculating the initial tension theoretical pulling-out amount △ L of the kth stay cableTheory of k，△LTheory of k＝Lk theory 1-Lk theory 2。
13. The verification device of claim 12, wherein L isk theory 1The determining of the sub-modules specifically comprises:
the two-end anchor point determining unit is used for acquiring deformed coordinate values of a tower-end anchor point and a beam-end anchor point when the stay cable is installed and is not subjected to primary tensioning according to a theoretical analysis result before the stay cable is subjected to primary tensioning in a preset theoretical parting model;
Lk theory 1A determining unit, configured to calculate, in a preset theoretical parting model, a distance L between a tower-end anchor point and a beam-end anchor point before installation of the stay cable according to coordinate values after deformation of the tower-end anchor point and the beam-end anchor point when the stay cable is not initially tensioned during installation of the stay cablek theory 1。
14. The verification device of claim 13, wherein L isk theory 2The determination submodule includes:
Tk theory 2A determining unit, configured to determine, in a preset theoretical analysis model, a theoretical initial tension value T required by the kth stay cable when the kth stay cable is tensioned to an initial tensioned statek theory 2；
Lk theory 2A determining unit for determining the theoretical value T of the initial tension required by the kth stay cable in a preset theoretical analysis modelk theory 2Analyzing the construction stage, and simulating the unstressed length L between anchor points when the kth stay cable is in place in the initial tensioning state when the kth stay cable is tensioned to the initial tensioning statek theory 2。
15. The verification device according to claim 14, wherein the initial tension actual pull-out amount acquisition module includes:
a marking submodule for marking the actual value F of the cable force of the kth stay cable when the kth stay cable is actually constructedk actualIs Tk theory 1And Tk theory 2Respectively marking the pulling-out amount of the stay cable;
△Lk actualA calculation submodule for calculating △ Lk actual，△Lk actualIs the length △ L between the marked pointsk actual；
Wherein, Tk theory 1And in a preset theoretical analysis model, when the length of the kth stay cable is the unstressed length, performing construction stage analysis, and simulating the cable force of the kth stay cable in the unstressed installation state.
16. The verification device according to claim 15, wherein the initial tension actual pull-out amount acquisition module further includes:
Tk theory 1The determining submodule is used for simulating and installing the kth stay cable according to the unstressed length in an installation state model of the full-bridge stay cable simulated by the cable unit, carrying out construction stage analysis and simulating to obtain the cable force T of the kth stay cable in an unstressed statek theory 1；
The preset theoretical analysis model comprises a model for simulating the installation state of the full-bridge stay cable by using a cable unit.
17. The verification device according to claim 16, wherein the initial tension actual pull-out amount acquisition module further includes:
Tk theory 2The determining submodule is used for installing each main beam segment of the cable-stayed bridge corresponding to a pair of stay cables in a cantilever assembling construction stage model of the main beam of the cable-stayed bridge, and simulating in stages according to main beam installation, stay cable installation and initial tensioning of the stay cables in place; determining the initial tension theoretical value of each stay cable by taking the closure of the main beam sections as a target;
and the preset theoretical analysis model comprises a model of the construction stage of assembling the main girder cantilever of the cable-stayed bridge.
18. The utility model provides a check-up system of cable-stay bridge suspension cable initial tension stage which characterized in that includes:
one or more processors;
storage means for storing one or more programs;
the one or more programs, when executed by the one or more processors, cause the one or more processors to implement a method of verifying an initial tension phase of a cable-stayed bridge cable according to any one of claims 1 to 10.
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