CN110807221A - Cable force calculation method based on equivalent force displacement method - Google Patents
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Abstract
The invention discloses a cable force calculation method based on an equivalent force displacement method, which comprises the following steps of: determining an initial state or a current state, a tensioning sequence and a target state of a cable system structure and acquiring data; then respectively calculating the cable force of a stay cable in the current state, the cable force of the stay cable in the target state, the deformation difference value of the linear distance between the upper anchor point and the lower anchor point of the stay cable in the current state relative to the initial state, and the deformation difference value of the linear distance between the upper anchor point and the lower anchor point of the stay cable in the target state relative to the initial state; then calculating the internal force increment required by the inhaul cable when the target state is reached; and finally, replacing the internal force increment required by the stay cable when the target state is reached by adding the internal force to obtain the cable force after cable adjustment in the current state, namely the tensile force required by field tensioning. The calculation method reduces the calculation complexity and the calculation amount, saves a large amount of calculation time, and improves the working efficiency.
Description
Technical Field
The invention relates to the technical field of bridge engineering, in particular to a cable force calculation method based on an equivalent force displacement method.
Background
The general span scale of cable-stayed bridge is very big, and the main component is girder, suspension cable and pylon, and the girder pressurized, the suspension cable pressurized belongs to high order hyperstatic structure, "pull a cable and move the full-bridge", and the system is constantly switched in the work progress moreover, therefore, whether accurate calculation and control of construction cable force will decide the cable-stayed bridge becomes the bridge state reasonable or not.
In general, the ideal bridge cable forming force is determined as a final target through cable force optimization, and then the reasonable construction cable force is determined according to a specific construction program. At present, the main methods for determining the reasonable construction cable force of the cable-stayed bridge are as follows: a reverse-dismantling method, a forward-assembling-reverse-dismantling iterative method, a forward-assembling iterative method, a stress-free state control method and the like.
The back-off method, the forward assembling-back-off iterative method and the stress-free state control method have the problem of non-closure in different degrees, namely, the forward assembling calculation is inconsistent with the reasonable bridging state when the forward assembling calculation is carried out according to the obtained construction state control parameters; although the forward-installed iteration method can effectively solve the problem of unclosed and does not need to perform reverse-dismantling calculation, the forward-installed iteration method needs to perform iterative calculation repeatedly for multiple times until the calculation result meets the requirement, the calculation workload of the method is large, and if the stay cable of the cable-stayed bridge needs to be tensioned and adjusted for multiple times, the cable force of the stay cable tensioned every time can be calculated only by performing repeated iteration for multiple times, so the calculation workload is undoubtedly greater, and a large amount of time is consumed.
Disclosure of Invention
The invention aims to provide a cable tension calculation method based on an equivalent force displacement method, which reduces the calculation complexity and the calculation amount, saves a large amount of calculation time and improves the working efficiency.
The technical scheme is as follows:
the cable force calculation method based on the equivalent force displacement method is characterized in that the cable force is replaced by an external load in a balanced state, the upper anchor point and the lower anchor point of the cable are displaced relative to the initial state in a target state, the linear distance change difference between the upper anchor point and the lower anchor point of the cable is obtained through the displacement value between the upper anchor point and the lower anchor point of the cable, and the tensile force required by tensioning the cable on site is further obtained, and the calculation method comprises the following steps:
a. determining an initial state or a current state, a tensioning sequence and a target state of the inhaul cable system structure, and acquiring data of the inhaul cable system structure in the initial state or the current state and the target state;
b. calculating the stay cable force F1 in the current state, the stay cable force F2 in the target state, and the deformation difference delta between the linear distance between the upper anchor point and the lower anchor point of the stay cable in the current state and the initial stateL1And the deformation difference value delta of the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the target state relative to the initial stateL2；
c. Calculating the internal force increment F required by the stay cable when the stay cable reaches the target state according to the linear distance between the upper anchor point and the lower anchor point of the stay cable, the elastic modulus of the stay cable, the cross sectional area of the stay cable, the cable force of the stay cable in the current state, the cable force of the stay cable in the target state, the deformation difference value of the linear distance between the upper anchor point and the lower anchor point of the stay cable in the current state relative to the initial state and the deformation difference value of the linear distance between the upper anchor point and the lower anchor point of the stay cable;
d. and replacing the internal force increment required by the stay cable when the target state is reached by adding the internal force to obtain the cable force after cable adjustment in the current state, namely the tension force required by field tension.
Further, in the step c, the following formula is adopted to calculate the internal force increment F required by the inhaul cable when the target state is reached;
wherein ,
wherein L is the linear distance between the upper and lower anchor points of the cable in the target state, and E is the elastic modulus of the cable (when the cable is a stay cable, the sag elastic modulus should be converted into Eernst) A is the cross-sectional area of the cable, F(virtual cable force part)The variable quantity of the cable force is caused by the deformation caused by the structural nonlinearity in the tensioning process.
Further, the calculation method substitutes the internal force increment required by the stay cable when the target state is reached into finite element software for calculation in a mode of adding the internal force, and the tensile force required by field tensioning is obtained.
The cable force calculation method based on the equivalent force displacement method is characterized in that in a target state, an upper anchor point and a lower anchor point of a cable are pulled back to initial state positions and are kept balanced, the structural form and the internal force state except the cable return to the initial state, the structure returns to the target state after being loosened, and the tensile force required by field tensioning is obtained through strain energy required by the cable reaching the target state in the initial state according to the law of conservation of energy, and the calculation method comprises the following steps:
a. determining an initial state or a current state, a tensioning sequence and a target state of the inhaul cable system structure, and acquiring data of the inhaul cable system structure in the initial state or the current state and the target state;
b. calculating the unstressed distance L between the upper anchor point and the lower anchor point of the inhaul cable according to the target cable force, the elasticity modulus of the inhaul cable and the cross section area of the inhaul cable0；
c. Calculating the cable force F in the initial state according to the unstressed distance between the upper anchor point and the lower anchor point of the stay cables；
d. Calculating the cable force F required by reaching the target state under the current state according to the variable quantity of the strain energy of the stay cable from the initial state to the current state, the unstressed distance between two anchor points of the stay cable and the cable force in the initial stateip；
e、The cable force in the current state is replaced and adjusted to be F in the form of in-vivo forceipAnd the formed rope force state force is the tensile force required by field tensioning in the current state.
Further, in the step b, a linear distance L between an upper anchor point and a lower anchor point of the inhaul cable under the target state is calculated firstlydThen, the following formula is adopted to calculate the unstressed distance L between the upper anchor point and the lower anchor point of the stay cable0：
wherein ,FdFor the target cable force, E is the elastic modulus (the elastic modulus E in terms of sag in the case of stay cableernst) And A is the cross-sectional area of the stay cable.
Further, in the step c, the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the initial state is calculated to be LsThen, the following formula is adopted to calculate the initial cable force Fs：
wherein ,L0Is a stress free spacing.
Further, in the step d, a linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the current state is calculated to be LipThen, the following formula is adopted to calculate the cable force F required by reaching the target state under the current stateip：
wherein ,FisIs an initial state cable force, LisIs the linear distance L between the upper anchor point and the lower anchor point of the inhaul cable in the initial stateipIs the linear distance between the upper anchor point and the lower anchor point in the current state, Li0The upper anchor point and the lower anchor point of the inhaul cable have no stress space.
Further, at a certain stage in a round of tuning according to the conservation of energyKnowing the linear distance L between anchor points of the current cableipInitial cable anchor point linear distance LisInitial cable force FisTarget cable force Fid。
The amount of change in strain energy from the initial state to the current state can be calculated from the amount of decrease in the linear distance between the cable anchors,
namely:
the amount of change in strain energy from the initial state to the current state is given by the following calculation formula:
the rope force F required for reaching the target state from the current state can be solved simultaneouslyipThe calculation formula of (2):
further, the calculation method carries out full displacement constraint on the upper anchor point and the lower anchor point of the current tension cable through finite element analysis software, and then replaces and adjusts the current cable force to be FipAnd then, the constraints of the upper anchor point and the lower anchor point are removed, and the formed cable force state force is the tension force required by the field tension of the inhaul cable in the current state.
According to the calculation method, the calculation result is subjected to replacement calculation by using finite element analysis software to obtain the tensile force required by field tensioning, and the adjusted cable force does not need to be adjusted on the premise that the target state of the subsequent batch of cables is not changed, namely all cables of the batch of cables can reach the target value of the batch of cables after one-time normal installation, so that the complex links in the cable adjusting process can be greatly reduced, and the problem of difficult cable adjustment is effectively solved; compared with methods such as forward-installation iteration, reverse-disassembly closing and the like, the method has the advantages of reducing the calculation amount, saving a large amount of calculation time and improving the working efficiency.
Drawings
Fig. 1 is an equivalent force model diagram of the cable in the embodiment of the invention, wherein the initial state of the cable is changed into the target state.
FIG. 2 is an equivalent force model diagram of the cable target state changing to the equivalent target state in the embodiment of the present invention.
FIG. 3 is a schematic diagram of a cable target state relative to an initial state in an embodiment of the invention.
Detailed Description
The following provides a detailed description of embodiments of the invention.
The invention obtains two cable force calculation methods based on the equivalent force displacement method, the calculation steps and the derivation processes of the two calculation methods are respectively described below, and the cable force calculation method based on the equivalent force displacement method is verified through specific application cases.
Explanation is first given to the state of the cable, the internal force and the external force:
initial state: the state before the structure is provided with the inhaul cable or the state that the structure finishes one-wheel cable adjustment.
The current state is as follows: the current state can be the initial state before a certain cable is stretched in a round of cable.
Target state: and completing the state required by the structure after one round of cable adjustment.
Internal force: the structure system is kept unchanged, the cable is stretched to a certain cable force before the cable is hung, the structure deforms together with the cable under the action of stress, and the deformed cable force is called as an internal force.
External force of body: before the cable is hung, a pair of external forces which are the same as the tension cable force are added at the cable hanging position to deform the structure, then the cable is independently tensioned to the tension cable force and then hung, and the cable force after the cable is hung is called as the external force.
Equivalent target state: and under the target state, the stay cable is removed from the state after the equivalent load is adopted for replacement.
The first cable force calculation method based on the equivalent displacement method comprises the following steps of replacing cable force by external load in a balanced state, enabling an upper anchor point and a lower anchor point of a cable to be displaced in a target state relative to an initial state, obtaining a linear distance change difference value between the upper anchor point and the lower anchor point of the cable according to a displacement value between the upper anchor point and the lower anchor point of the cable, and further obtaining the tensile force required by tensioning the cable on site, wherein the calculation method comprises the following steps:
a. determining an initial state or a current state, a tensioning sequence and a target state of the inhaul cable system structure, and acquiring data of the inhaul cable system structure in the initial state or the current state and the target state;
b. according to the equivalent model, calculating the cable force F1 of the cable in the current state, the cable force F2 of the cable in the target state and the deformation difference delta between the linear distance between the upper anchor point and the lower anchor point of the cable in the current state relative to the initial state at the end of the construction step in the previous stage by finite element analysis softwareL1And the deformation difference value delta of the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the target state relative to the initial stateL2(ii) a The equivalent efficacy model is shown in figure 1.
c. According to the linear distance between the upper anchor point and the lower anchor point of the inhaul cable, the elastic modulus of the inhaul cable, the cross-sectional area of the inhaul cable, the inhaul cable force in the current state, the inhaul cable force in the target state, the deformation difference value of the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the current state relative to the initial state and the deformation difference value of the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the target state relative to the initial state, the internal force increment F required by the inhaul:
wherein ,
wherein L is the linear distance between the upper and lower anchor points of the cable in the target state, and E is the elastic modulus of the cable (when the cable is a stay cable, the sag elastic modulus should be converted into Eernst) And A is the cross section area of the stay cable.
Note that: when there is other load or action besides the self-weight of the structure in the process, and the position, size and direction of the action or load in the comparison between the initial state and the target state are changed, the nonlinear influence of the structure caused by the change of the action or load should be considered in the equivalent process, and the influence should be taken into account in the virtual cable force part.
d. And substituting the internal force increment required by the stay rope when the stay rope reaches the target state into finite element software for calculation in a mode of adding the internal force, so as to obtain the calculated state rope force of the adjusted rope at the current stage, wherein the obtained state rope force is the tensile force required by field tensioning. On the premise that the target state of the subsequent batch of cables is not changed, the cable force does not need to be adjusted, namely all cables of the batch of cables can reach the target value of the batch of cables according to the method after one-time normal installation.
Note that: the influence of shrinkage and creep in the related process can be synchronously considered in finite element software, namely the time length effect of the shrinkage and creep is considered in the calculation of the equivalent force target value, and the influence is taken into account in the virtual cable force caused by the structure deformation difference.
The derivation process of the first equivalent force displacement method-based cable force calculation method is as follows:
adding unequal force values F to all the cables simultaneously in the equivalent target state (the state shown in FIG. 2)xThe linear distance between the upper anchor point and the lower anchor point of the inhaul cable can be pulled back to the linear distance in the initial state. According to the principle of structural elasticity, FxAfter being unloaded, the equivalent target state is recovered. Defining unequal force values F in the present inventionxThe cable force is virtualized for structural deformation. On the contrary, each cable is added with a size F ═ F at the same time in the initial statexThe target state can be reached by applying the in vivo force of + F2 to the structure. By derivation, FxThe calculation formula of (a) is as follows:
wherein F2 is the internal force of the cable in the target state; e is the elastic modulus of the stay cable, and when the stay cable is a stay cable, the sag should be converted into Eernst(ii) a A is the cross section area of the stay cable; deltaL2Is a straight line between upper and lower anchor points of the inhaul cable under the target stateDifference in deformation of distance from the initial state, ΔL1The deformation difference value of the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the current state relative to the initial state is obtained; and L is the linear distance between the upper anchor point and the lower anchor point of the inhaul cable under the target state.
In actual construction, one round of cable adjustment is usually carried out step by step according to a certain sequence. Under the condition of determining the initial state, the cable adjusting sequence and the target state, the internal force increment required by each cable from the current state to the target state can be calculated:
wherein F is the internal force of the cable in the current state.
And adding the calculated internal force increment to the current state, and obtaining the internal force after cable adjustment in the current state after the structural deformation is coordinated with each other, wherein the internal force can be regarded as the external force of the current tension cable, namely the tension force required during field tension. If the target state is not changed, the cable is not required to be adjusted in the subsequent cable adjustment.
According to the cable force calculation method based on the equivalent force displacement method, the external load is applied to replace the cable force in a balanced state, the deformation of the structure in a target state relative to the initial state in the equivalent cable force state is checked, and the deformation difference of the linear distance between the upper anchor point and the lower anchor point of the cable from the initial state to the target state is calculated according to the deformation amount. The cable force calculated by the deformation difference is defined as a virtual cable force, namely the change of the cable force caused by the deformation caused by the structural nonlinearity in the tensioning process.
The second cable force calculation method based on the equivalent displacement method comprises the following steps of pulling the upper anchor point and the lower anchor point of the cable back to the initial state positions and keeping balance in a target state, returning the structural form and the internal force state except the cable to the initial state, recovering the target state after loosening, and obtaining the tensile force required by field tensioning through the strain energy required by the cable in the initial state to reach the target state according to the law of conservation of energy, wherein the calculation method comprises the following steps:
a. determining an initial state or a current state, a tensioning sequence and a target state of the inhaul cable system structure, and acquiring data of the inhaul cable system structure in the initial state or the current state and the target state;
b. firstly, the linear distance L between the upper anchor point and the lower anchor point of the inhaul cable under the target state is calculateddAccording to the target cable force, the elastic modulus of the stay cable and the cross-sectional area of the stay cable, the unstressed distance L between the upper anchor point and the lower anchor point of the stay cable is calculated by adopting the following formula0：
wherein ,FdFor the target cable force, E is the elastic modulus (the elastic modulus E in terms of sag in the case of stay cableernst) A is the cross-sectional area of the stay cable;
c. firstly, the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the initial state is calculated to be LisThen, according to the unstressed distance between the upper anchor point and the lower anchor point of the stay cable, the following formula is adopted to calculate and calculate the cable force F in the initial states：
wherein ,L0Is a stress free spacing;
d. firstly, calculating the linear distance L between the upper anchor point and the lower anchor point of the inhaul cable under the current stateipAccording to the unstressed distance between the upper anchor point and the lower anchor point of the stay cable and the cable force in the initial state, the following formula is adopted to calculate the cable force F required by reaching the target state in the current stateip：
wherein ,FisIs an initial state cable force, LisIs the linear distance L between the upper anchor point and the lower anchor point of the inhaul cable in the initial stateipIs the linear distance between the upper anchor point and the lower anchor point in the current state, Li0Is pulling aThe upper anchor point and the lower anchor point of the cable have no stress space.
e. The upper anchor point and the lower anchor point of the inhaul cable in the current state are subjected to full displacement constraint, and then the current cable force is replaced and adjusted to be F in the form of in-vivo forceipAnd then, removing the constraint of the upper anchor point and the lower anchor point, wherein the formed cable force state force is the tension force required by the cable field tensioning in the current state.
The derivation process of the second equivalent force displacement method-based cable force calculation method is as follows:
assuming that the total potential energy inside the structure in the initial state (without the cable structure part) is E0The internal potential energy of the structure is changed into E under the action of the cable force under the target state (without the cable structure part)dThe amount of change (Δ) in the structure potential in this processEd＝Ed-E0) Equal to the total strain energy sigma U of the stay cable when the upper and lower anchor points of the stay cable are pulled back to the initial state positions in the target stateisAnd the total strain energy sigma U of the stay cable under the target stateidThe difference, i.e. DeltaEd＝Ed-E0＝∑Uis-∑Uid。
Because the potential energy increment from the initial state of the structure to the target state is considered, the actual state potential energy of the structure does not need to be considered, and the increment of converting the strain energy into the structure potential energy when the cable force changes needs to be considered, namely deltaEd＝∑Uis-∑Uid。
Under the initial structure state of the structure, the total strain energy of the guy cable which can lead the structure to reach the target state is defined as follows:
the total strain energy of the stay cable under the target state is as follows:
wherein i is the number of the cables, and n is the number of the cables.
Calculation of strain energy of stay cableThe formula is as follows:
when the F and the A are known,wherein L is the linear distance between the upper and lower anchor points when no stress exists, F is the cable force, and E is the elastic modulus (the elastic modulus E is converted into the elastic modulus considering the sag when the cable is inclinedernst) And A is the area of the stay cable.
Since the cable force of the target state is known, the linear distance L between the upper anchor point and the lower anchor point of the stay cable under the target state can be calculated according to the equivalent force model (as shown in figure 2)d。
According to the target cable force FdThe unstressed distance between the upper anchor point and the lower anchor point of the cable can be calculated as
The linear distance between the upper anchor point and the lower anchor point of the cable is L in the initial statesCorresponding to a cable force of Fs. Due to L0Known and easy to calculate
Therefore, under the initial structure state of the structure, the strain energy of the single guy cable which can enable the structure to reach the target state is as follows:
the strain energy corresponding to a single cable in a target state is as follows:
then, in the initial state of the structure, the total strain energy difference of the guy cable which can enable the structure to reach the target state is as follows:
as can be seen from the above formula, the strain energy of the single cable is converted into
At a certain stage in one-round cable adjustment, the linear distance L between anchor points of the current cable is knownipInitial cable anchor point linear distance LisInitial cable force FisTarget cable force Fid。
The amount of change in strain energy from the initial state to the current state can be calculated from the amount of decrease in the linear distance between the cable anchors,
namely:
meanwhile, according to the calculation formula of the difference value of the strain energy in two different states, the variable quantity of the strain energy from the initial state to the current state is as follows:
simultaneously, the cable force required to reach the target state from the current state can be solved:
Fipthe cable force is required to reach the target state under the current state, and new transformation from strain energy to structure potential energy is generated due to the deformation of the structure nonlinearity of the cable force in the actual tensioning process, and the specific current actual tensioning force target value is still unknown. Therefore, only in the finite element simulation process, the full displacement constraint can be carried out on the upper anchor point and the lower anchor point of the current tensioned cable, and then the current cable force is replaced and adjusted to be FipThen, the upper and lower anchor point constraints are removed, and the formed cable force state force is the current cable tensionA target value.
The isoeffect displacement method can utilize the calculated internal force value (increment) to substitute finite element software for calculation, so that the calculated state cable force of the adjusted cable in the current stage can be obtained, the obtained state cable force is the tensile force required by field tensioning and also becomes the external force, the adjusted cable force does not need to be adjusted on the premise that the subsequent target state of the batch of the adjusted cables is not changed, namely all cables of the batch of the adjusted cables can reach the target value of the batch of the adjusted cables according to the method after one-time normal installation, the influence of shrinkage creep in the related process can be synchronously considered in the finite element software, namely the effect of the time length of the shrinkage creep is considered in the calculation of the target value of the isoeffect, and the influence is counted into the virtual cable force caused by the structural deformation difference.
The two calculation methods can solve the complex and tedious cable adjustment problem, and the required tension cable force can be calculated only by determining the initial state (or the current state) and the target state of the structure, wherein the target state can be the target state of cable force stage tension or the final bridge target state.
Due to the fact that the equivalent force is added into the finite element model conveniently and the displacement of each node of the structure at each stage is convenient to check, the method can greatly reduce the complex links in the process of cable adjustment, and effectively solves the problem of difficult cable adjustment; compared with the original methods of forward-assembling iteration, reverse-disassembling closing and the like, the method saves a large amount of process calculation time, improves the working efficiency and can also test the structural state of each stage.
The cable force calculation method based on the equivalent force displacement method is suitable for calculating the cable force of a conventional cable-stayed bridge cable, the cable force of a tied arch bridge suspender and the cable force of a small-deformation cable system structure with a similar structure.
In this embodiment, a continuous girder arch bridge with a span combination of (64+136+64) m is selected as a specific application case, and the cable force calculation method based on the equivalent force displacement method is verified, where the specific application case is as follows:
the bridge adopts a construction mode of 'first beam, then arch and finally suspender', the main beam is constructed by adopting cantilever casting, arch ribs are erected on the closed main beam by adopting a support, the suspender is tensioned for three times, and the bridge reaches a target bridge forming state after the suspender is tensioned for the last time. The boom tensioning sequence and boom force values are shown in table 1.
TABLE 1 boom tensioning sequence and boom force values
In one process, all the suspenders are stretched by adopting the tension of 150kN, so that the problem of suspender tension calculation does not exist in one process. In the example, the invention is mainly applied to the two-sheet stage and the three-sheet stage, and Midas/Civil is adopted to perform modeling calculation in the embodiment, and the specific implementation steps are as follows:
the first step is as follows: analyzing the initial state of the suspender before activation, namely calculating the linear distance L between the upper anchor point and the lower anchor point of the suspender after arch rib construction is finished1The calculation results are shown in table 2. The initial state of the boom prior to activation is shown in fig. 1.
The second step is that: and carrying out state analysis when the force of the two target lifting rods is reached. Knowing that the target state force of the two rear suspenders is 150kN, adding 150kN of equal-effect load to the initial state model before the suspenders are activated, and calculating the linear distance L between the upper anchor point and the lower anchor point of the suspenders when the target state force of the two suspenders reaches the two target state model2The calculation results are shown in table 2, and the state when two target boom forces are reached is shown in fig. 2.
TABLE 2 displacement calculation results (unit: mm) of upper and lower anchor points in the state before boom activation and in the state of two targets
The third step: a post-sheet state analysis was performed, in which the booms were activated in a predetermined tension order, and a tensile force of 150kN was given to each boom by an external body force while each boom was activated, and the results of calculation of the internal force of the boom after a sheet were shown in fig. 3.
The fourth step: and calculating the tension of the boom D1. Before calculation, the state of boom D1 two times before is defined as the current state. In fact, the analysis of the state of the boom D1 before being tensioned has been completed in the third step, and therefore the amount of change Δ in the linear distance between the upper and lower anchor points of the boom D1 at the current stage in the state before being tensioned is the boom D1LD1 (Current)Current state internal force FD1 (Current)All known, the result query can yield ΔLD1 (Current)＝2.70mm，FD1 (Current)＝94.2kN。
Knowing the target State internal force F of the two rear boom D1D1 (goal)Table 1 shows the amount of change Δ in the linear pitch between the upper and lower anchor points when the boom D1 reaches the two-piece target state, i.e., 150kNLD1 (goal)The increase in body force required to reach the two target states of boom D1 can be calculated as follows, 5.06 mm.
Calculated, FD1 (internal force increment required to reach two target forces)＝173kN。
Then adding F by means of in vivo forceD1 (internal force increment required to reach two target forces)Substituting the obtained tension into the model, and calculating to obtain the tension F required by the suspender D1 when the suspender D1 reaches the two-piece target stateD1＝223.6kN。
The fifth step: and calculating the tension of the boom D3. Since the calculation is performed based on the state after two booms D1 when the boom D3 is tensioned two by two, the state after two booms D1 is defined as the current state. In the calculation, the state of the boom D1 after two is determined, and F is measured in the mode of external force in the model after oneD1Endowing the suspender D1 with the linear distance variation delta between the upper anchor point and the lower anchor point of the suspender D1 at the current stage under the state before tensioning the suspender D1LD3 (Current)Current state internal force F of 3.53mmD3 (Current)＝0kN。
Knowing the target State internal force F of the two rear boom D3D3 (goal)150kN, as can be seen from Table 1Change delta of linear distance between upper anchor point and lower anchor point when rod D3 reaches two-target stateLD3 (goal)The increase in body force required to reach the two target states of boom D3 can be calculated according to the formula in the fourth step, which is 17.91 mm. Calculated, FD3 (internal force increment required to reach two target forces)＝417kN。
Then adding F by means of in vivo forceD3 (internal force increment required to reach two target forces)Substituting the obtained tension into the model, and calculating to obtain the tension F required by the suspender D3 when the suspender D3 reaches the two-piece target stateD3＝314.5kN。
And a sixth step: and calculating the tension of the suspenders D5, D7, D2, D4 and D6 according to the steps, and finally, after the suspenders are tensioned to D6, the two target cable forces are achieved without repeated iteration.
The seventh step: and D1-D7 tension force of the three suspension rods is calculated. The three-piece and two-piece basic calculation processes are the same, the initial state is the same, the target state is equivalent to three target tension forces, the actual conditions of bridge deck pavement increase, midspan two-stage prestressed tendon tensioning, side-span pressure weight removal and the like are considered, other tensioning sequences and one-time calculation methods are not different, and the description is omitted.
According to a mature and widely applied formal iterative calculation method, checking and calculating by an equivalent force displacement method, wherein basic models adopted in the calculation are consistent, parameters are set consistently, and the final results are compared as follows:
TABLE 3 comparison of two tension results with the upright iteration results
TABLE 4 comparison of the three tension results with the formal iteration result
According to the comparison of calculation results and the forward-installation iteration method, the deviation can be basically controlled within a small range after enough iterations, and the maximum deviation of the formed bridge is within 2% after one-time forward-installation of the equivalent-effect displacement calculation method, so that the standard requirement is met.
According to the fact that the tension forces (external forces) obtained through calculation in the embodiment are basically consistent, the calculated target state forces are basically consistent, and the cable force calculation method based on the equivalent force displacement method is proved to be feasible.
The above examples are merely representative of specific embodiments of the present invention, and the description thereof is more specific and detailed, but not to be construed as limiting the scope of the present invention. It should be noted that various alternatives, modifications and variations can be devised by those skilled in the art without departing from the spirit and scope of the invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (9)
1. The cable force calculation method based on the equivalent force displacement method is characterized in that the cable force is replaced by an external load in a balanced state, the upper anchor point and the lower anchor point of the cable are displaced relative to the initial state in a target state, the linear distance change difference between the upper anchor point and the lower anchor point of the cable is obtained through the displacement value between the upper anchor point and the lower anchor point of the cable, and the tensile force required by tensioning the cable on site is further obtained, and the calculation method comprises the following steps:
a. determining an initial state or a current state, a tensioning sequence and a target state of the inhaul cable system structure, and acquiring data of the inhaul cable system structure in the initial state or the current state and the target state;
b. calculating the stay cable force F1 in the current state, the stay cable force F2 in the target state, and the deformation difference delta between the linear distance between the upper anchor point and the lower anchor point of the stay cable in the current state and the initial stateL1And the deformation difference value delta of the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the target state relative to the initial stateL2；
c. Calculating the internal force increment F required by the stay cable when the stay cable reaches the target state according to the linear distance between the upper anchor point and the lower anchor point of the stay cable, the elastic modulus of the stay cable, the cross sectional area of the stay cable, the cable force of the stay cable in the current state, the cable force of the stay cable in the target state, the deformation difference value of the linear distance between the upper anchor point and the lower anchor point of the stay cable in the current state relative to the initial state and the deformation difference value of the linear distance between the upper anchor point and the lower anchor point of the stay cable;
d. and replacing the internal force increment required by the stay cable when the target state is reached by adding the internal force to obtain the cable force after cable adjustment in the current state, namely the tension force required by field tension.
2. The cable force calculation method based on the equivalent force displacement method according to claim 1, wherein the following formula is adopted in the step c to calculate the internal force increment F required by the cable when the target state is reached;
wherein ,
wherein L is the linear distance between the upper and lower anchor points of the cable in the target state, and E is the elastic modulus of the cable (when the cable is a stay cable, the sag elastic modulus should be converted into Eernst) A is the cross-sectional area of the cable, F(virtual cable force part)The variable quantity of the cable force is caused by the deformation caused by the structural nonlinearity in the tensioning process.
3. The cable force calculation method based on the equivalent force displacement method as claimed in any one of claims 1 to 2, wherein the calculation method substitutes the increment of the internal force required by the cable when the target state is reached into finite element software for calculation in a mode of adding the internal force, and obtains the tensile force required by field tensioning.
4. The cable force calculation method based on the equivalent force displacement method is characterized in that in a target state, an upper anchor point and a lower anchor point of a cable are pulled back to initial state positions and are kept balanced, the structural form and the internal force state except the cable return to the initial state, the structure returns to the target state after being loosened, and the tensile force required by field tensioning is obtained through strain energy required by the cable reaching the target state in the initial state according to the law of conservation of energy, and the calculation method comprises the following steps:
a. determining an initial state or a current state, a tensioning sequence and a target state of the inhaul cable system structure, and acquiring data of the inhaul cable system structure in the initial state or the current state and the target state;
b. calculating the unstressed distance L between the upper anchor point and the lower anchor point of the inhaul cable according to the target cable force, the elasticity modulus of the inhaul cable and the cross section area of the inhaul cable0；
c. Calculating the cable force F in the initial state according to the unstressed distance between the upper anchor point and the lower anchor point of the stay cables；
d. Calculating the cable force F required by reaching the target state under the current state according to the variable quantity of the strain energy of the stay cable from the initial state to the current state, the unstressed distance between two anchor points of the stay cable and the cable force in the initial stateip；
e. The cable force in the current state is replaced and adjusted to be F in the form of in-vivo forceipAnd the formed rope force state force is the tensile force required by field tensioning in the current state.
5. The cable force calculation method based on the equivalent force displacement method of claim 4, wherein in the step b, the linear distance L between the upper anchor point and the lower anchor point of the cable under the target state is calculated firstdThen, the following formula is adopted to calculate the unstressed distance L between the upper anchor point and the lower anchor point of the stay cable0：
wherein ,FdThe target cable force is E, and the elastic modulus (converted into consideration in the case of stay cable)Modulus of elasticity E of sagernst) And A is the cross-sectional area of the stay cable.
6. The cable force calculation method based on the equivalent force displacement method of claim 4, wherein the linear distance between the upper anchor point and the lower anchor point of the cable in the initial state is calculated as L in the step cisThen, the following formula is adopted to calculate the initial cable force Fs：
wherein ,L0For unstressed spacing, E is the elastic modulus (elastic modulus E converted to sag consideration in stay cables)ernst) And A is the cross-sectional area of the stay cable.
7. The cable force calculation method based on the equivalent force displacement method of claim 4, wherein the linear distance between the upper anchor point and the lower anchor point of the cable under the current state is calculated as L in the step dipThen, the following formula is adopted to calculate the cable force F required by reaching the target state under the current stateip：
wherein ,FisIs an initial state cable force, LisIs the linear distance L between the upper anchor point and the lower anchor point of the inhaul cable in the initial stateipIs the linear distance between the upper anchor point and the lower anchor point in the current state, Li0The upper and lower anchor points of the stay are free of stress, and E is the elastic modulus (the elastic modulus E is converted into the elastic modulus considering sag when the stay cable is inclinedernst) And A is the cross-sectional area of the stay cable.
8. The cable force calculation method based on the equivalent force displacement method as claimed in claim 7, wherein the linear distance L between anchor points of the current cable is known at a certain stage in a round of cable adjustment according to energy conservationipInitial cable anchor pointDistance L between straight linesisInitial cable force FisTarget cable force Fid。
The amount of change in strain energy from the initial state to the current state can be calculated from the amount of decrease in the linear distance between the cable anchors,
namely:
the variable quantity of the strain energy from the initial state to the current state is again:
the two formulas are combined to solve the cable force F required by reaching the target state from the current stateipThe calculation formula of (2):
9. the cable force calculation method based on the equivalent force displacement method as claimed in any one of claims 4 to 8, wherein the calculation method carries out full displacement constraint on the upper anchor point and the lower anchor point of the current tension cable through finite element analysis software, and then the replacement and adjustment of the current cable force are carried out to be FipAnd then, the constraints of the upper anchor point and the lower anchor point are removed, and the formed cable force state force is the tension force required by the field tension of the inhaul cable in the current state.
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