CN110807221B - 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: firstly, 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 in the current state, the 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 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 cable in the target state relative to the initial state; then calculating the internal force increment required by the inhaul cable when the inhaul cable reaches the target state; and finally, replacing the internal force increment required by the inhaul cable when the inhaul cable reaches the target state in a mode of adding the internal force to obtain the cable force after the cable is regulated in the current state, namely the tension force required by field tension. 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 the cable-stayed bridge is very large, the main components are a main girder, a stay cable and a cable tower, the main girder is stressed, the stay cable is stressed, the cable-stayed bridge belongs to a high-order statically indeterminate structure, "one cable is pulled to move the full bridge", and the system is continuously converted in the construction process, so that whether the construction cable force can be accurately calculated and controlled can determine whether the cable-stayed bridge is in a reasonable state.
Under the general condition, the optimal bridge forming cable force is firstly determined through cable force optimization as a final target, and then the reasonable construction cable force is determined according to a specific construction program. At present, the main method for determining the reasonable construction cable force of the cable-stayed bridge comprises the following steps: an inverted disassembly method, a forward assembly-inverted disassembly iteration method, a forward assembly iteration method, a stress-free state control method, and the like.
The reverse disassembly method, the forward assembly-reverse disassembly iteration method and the stress-free state control method have the problem of non-closure to different degrees, namely the forward assembly calculation is inconsistent with the reasonable bridge forming state according to the obtained construction state control parameters, and in addition, the two methods need to perform reverse disassembly calculation, so that the calculation workload is greatly increased; the forward iterative method can effectively solve the problem of unclosed and does not need to carry out reverse disassembly calculation, but the forward iterative method needs to carry out iterative calculation repeatedly for a plurality of times until the calculation result meets the requirement, the calculation workload of the method is large, and if the guy cable of the cable-stayed bridge needs to be tensioned and adjusted for a plurality of times, the guy cable force of each tensioning can be calculated only by carrying out repeated iteration for a plurality of times, so that the calculation workload is huge undoubtedly, and a large amount of time is consumed.
Disclosure of Invention
The invention aims to provide a cable force 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 calculation method is characterized in that the cable force is replaced by an external load in a balanced state, the target state is opposite to the initial state, the upper anchor point and the lower anchor point of the cable are displaced, the linear distance change difference value 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 further the tension force required by on-site tensioning of the cable is 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 cable system structure, and acquiring data of the initial state or the current state and the target state of the cable system structure;
b. calculating the deformation difference delta 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, wherein the inhaul cable force F1 in the current state, the inhaul cable force F2 in the target state and the inhaul cable in the current state L1 Deformation difference delta of linear distance between upper anchor point and lower anchor point of inhaul cable in target state relative to initial state L2 ；
c. Calculating an internal force increment F required by the inhaul cable when the inhaul cable reaches the target state 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;
d. and replacing the internal force increment required by the inhaul cable when the inhaul cable reaches the target state by adding the internal force to obtain the cable force after the cable is regulated 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 inhaul cable reaches the target state;
wherein ,
where L is the linear distance between the upper and lower anchor points of the cable in the target state, E is the elastic modulus of the cable (when the cable is a stay cable, the sag elastic modulus is converted into E ernst ) A is the cross-sectional area of the inhaul cable, F (virtual Cable force part) Is the variation of the cable force caused by the deformation of the structure caused by nonlinearity in the tensioning process.
Further, the calculation method substitutes the internal force increment required by the inhaul cable when the inhaul cable reaches the target state into finite element software for calculation in a mode of adding internal force, and the stretching force required by on-site stretching 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 an initial state position, balance is maintained, the structural form and an internal force state except the cable are returned to the initial state, the structure is restored to the target state after being released, and the tension force required by on-site tensioning is obtained through the strain energy required by the cable 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 cable system structure, and acquiring data of the initial state or the current state and the target state of the cable system structure;
b. according to the target cable force, the elastic modulus of the cable and the cross section area of the cable, calculating the stress-free distance L between the upper anchor point and the lower anchor point of the cable 0 ；
c. According to the stress-free distance between the upper anchor point and the lower anchor point of the inhaul cable, calculating the cable force F in the initial state s ；
d. According to the change amount of strain energy from the initial state to the current state of the inhaul cable, the stress-free distance between two anchor points of the inhaul cable and the cable force in the initial state, calculating the cable force F required by reaching the target state in the current state ip ：
e. Replacement and adjustment of the cable force in the current state as an in-vivo force ip The formed cable force state force is the tension force required by field tensioning in the current state.
Further, in the step b, the linear distance L between the upper anchor point and the lower anchor point of the inhaul cable in the target state is calculated first d Then the stress-free distance L between the upper anchor point and the lower anchor point of the inhaul cable is calculated by adopting the following formula 0 ：
wherein ,Fd For the target cable force, E is the elastic modulus (the elastic modulus E is converted into the elastic modulus E considering sagging in stay cable ernst ) A is the cross-sectional area of the inhaul cable.
Further, in the step c, a linear distance L between an upper anchor point and a lower anchor point of the inhaul cable in an initial state is calculated s Then the following formula is adopted to calculate the initial cable force F s ：
wherein ,L0 Is stress-free spacing.
Further, in the step d, the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the current state is calculated to be L ip Then the following formula is adopted to calculate the cable force F required by reaching the target state in the current state ip ：
wherein ,Fis For the initial state of cable force L is Is the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the initial state, L ip Is the straight line distance between the upper anchor point and the lower anchor point in the current state, L i0 The stress-free distance between the upper anchor point and the lower anchor point of the inhaul cable is not provided.
Further, the linear distance L between the anchor points of the current cable is known at a certain stage in one round of cable adjustment according to energy conservation ip Straight line distance L between initial cable anchor points is Initial cable force F is Target cable force F id 。
The amount of change in strain energy from the initial state to the current state can be calculated from the decrease in linear distance between the cable anchor points,
namely:
the amount of change in strain energy from the initial state to the current state is known from the following calculation formula:
simultaneously, the cable force F required by the target state from the current state can be solved ip Is calculated according to the formula:
further, the calculation method carries out full displacement constraint on the upper anchor point and the lower anchor point of the current tensioning cable through finite element analysis software, and then replaces and adjusts the current cable force to F ip And then, the restraint of the upper anchor point and the lower anchor point is released, and the formed cable force state force is the stretching force required by the on-site stretching of the inhaul cable in the current state.
According to the calculation method, the calculation result is replaced and calculated by utilizing finite element analysis software, so that the tension force required by on-site tension is obtained, and the cable force is not required to be adjusted on the premise that the target state of the cable is unchanged in the follow-up batch of cable adjustment, namely all cables in the batch of cable adjustment can reach the target value of the cable adjustment in the batch of cable adjustment after one-time normal installation according to the method, so that complex links in the cable adjustment process can be greatly reduced, and the problem of cable adjustment difficulty is effectively solved; compared with methods such as forward assembly iteration, reverse disassembly and closure, the method reduces the calculated amount, saves a large amount of calculation time and improves the working efficiency.
Drawings
FIG. 1 is a diagram of an equivalent force model for changing the initial state of a cable to the target state in an embodiment of the present invention.
FIG. 2 is a diagram of an equivalent force model for changing a cable target state to an equivalent target state in an embodiment of the present invention.
Fig. 3 is a schematic diagram of a target state versus an initial state of a cable according to an embodiment of the invention.
Detailed Description
The following describes embodiments of the present invention in detail.
The invention provides two cable force calculation methods based on an equivalent force displacement method, wherein the calculation steps and the deduction processes of the two calculation methods are respectively shown below, and the cable force calculation method based on the equivalent force displacement method is verified through specific application cases.
Firstly, explaining the state of a guy rope, internal force and external force:
initial state: the state before the structure is installed with the inhaul cable or the state that the structure is completed with one round of rope adjusting.
Current state: the current state can be the initial state before stretching a certain inhaul cable in one round of cable adjusting.
Target state: and finishing the state required to be reached by the structure after one round of cable adjusting.
Internal force: the structural system is kept unchanged, the cable is tensioned to a certain cable force before being hung, the cable is hung, the structure and the cable are deformed together under the action of stress, and the deformed cable force is called as in-vivo force.
External force: before the cable is hung, a pair of external forces which are the same as the tension force of the cable are added at the position of the cable to deform the structure, and then the cable is independently tensioned to the tension force of the cable to be hung, and the cable force after the cable is hung is called as external force.
Equivalent target state: and removing the inhaul cable from the state of replacing the inhaul cable with the equivalent load under the target state.
According to the first cable force calculation method based on the equivalent force displacement method, cable force is replaced by externally adding load in a balanced state, the target state is opposite to the initial state, the upper anchor point and the lower anchor point of the cable are displaced, the linear distance change difference value 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 further the tension force required by the field tension cable is 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 cable system structure, and acquiring data of the initial state or the current state and the target state of the cable system structure;
b. according to the equivalent force model, calculating the deformation difference delta of the linear distance between the upper anchor point and the lower anchor point of the inhaul cable relative to the initial state by finite element analysis software, wherein the inhaul cable force F1 in the current state, the inhaul cable force F2 in the target state and the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the current state are at the end of the construction step of the upper stage L1 Deformation difference delta of linear distance between upper anchor point and lower anchor point of inhaul cable in target state relative to initial state L2 The method comprises the steps of carrying out a first treatment on the surface of the The equivalent force model is shown in the principle of 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 in-vivo force increment F required by the inhaul cable when reaching the target state is calculated by adopting the following formula:
wherein ,
where L is the linear distance between the upper and lower anchor points of the cable in the target state, E is the elastic modulus of the cable (when the cable is a stay cable, the sag elastic modulus is converted into E ernst ) A is the cross-sectional area of the cable.
Note that: when other loads or actions are applied in the process besides the self weight of the structure, and the position, the size and the direction of the loads are changed under the comparison of the initial state and the target state, the nonlinear structural influence caused by the change of the loads should be considered in the equivalent process, and the influence should be considered in the virtual cable force part.
d. Substituting the internal force increment required by the inhaul cable when reaching the target state into finite element software for calculation in a mode of adding internal force, and obtaining the calculated state cable force of the cable regulated at the current stage, wherein the obtained state cable force is the tensioning force required by field tensioning. The cable force is not required to be adjusted on the premise that the target state of the cable is unchanged in the follow-up batch of cables, namely all cables in the batch of cables can reach the target value of the batch of cables after one-time normal assembly.
Note that: the influence of the shrinkage creep in the related process can be synchronously considered in finite element software, namely the effect of the equal shrinkage creep duration is considered when the equal efficacy target value is calculated, and the influence is taken into account in the virtual cable force caused by the structural deformation difference.
The derivation process of the first cable force calculation method based on the equivalent force displacement method is as follows:
in the equivalent target state (the shape shown in FIG. 2State) to add unequal force value F to all cables simultaneously x The 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. F according to the principle of structural elasticity x After the unloading, the equivalent target state is restored. In the present invention, unequal force values F are defined x Virtual cable force is deformed for the structure. Conversely, in the initial state, each inhaul cable is added with a value of F=F at the same time x The internal force of +F2, the structure can reach the target state after application. Derived, F x The calculation formula of (2) 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 conversion should be considered as E ernst The method comprises the steps of carrying out a first treatment on the surface of the A is the cross section area of the inhaul cable; delta L2 Is the deformation difference 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 state L1 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 is obtained; l is the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the target state.
In actual construction, one round of cable adjusting is often carried out step by step according to a certain sequence. Under the condition of defining initial state, cable adjusting sequence and 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 into the current state, and obtaining the internal force of the cable after the cable is adjusted in the current state after the structural deformation is mutually coordinated, wherein the internal force can be regarded as the external force of the cable, namely the stretching force required by on-site stretching. If the target state is unchanged, the cable does not need to be adjusted in the subsequent cable adjusting process.
According to the cable force calculation method based on the equivalent force displacement method, the cable force is replaced by an additional load in a balanced state, deformation of the structure relative to an initial state in an equivalent cable force state in a target state is checked, and a deformation difference of a linear distance between an upper anchor point and a lower anchor point of the cable in the initial state and the target state is calculated by the deformation amount. The calculated cable force of the deformation difference is defined as a virtual cable force, namely the variation of the cable force caused by deformation due to structural nonlinearity in the tensioning process.
The second cable force calculation method based on the equivalent force displacement method, in the target state, the upper and lower anchor points of the inhaul cable are pulled back to the initial state position, balance is maintained, the structural form and the internal force state except the inhaul cable are all returned to the initial state, the structure is restored to the target state after being released, and the tension force required by the on-site tensioning is obtained through the strain energy required by the inhaul cable to reach the target state in the initial state according to the energy conservation law, 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 cable system structure, and acquiring data of the initial state or the current state and the target state of the cable system structure;
b. firstly, calculating the linear distance L between the upper anchor point and the lower anchor point of the inhaul cable in the target state d According to the target cable force, the elastic modulus of the cable and the cross section area of the cable, the stress-free distance L between the upper anchor point and the lower anchor point of the cable is calculated by adopting the following formula 0 ：
wherein ,Fd For the target cable force, E is the elastic modulus (the elastic modulus E is converted into the elastic modulus E considering sagging in stay cable ernst ) A is the cross section area of the inhaul cable;
c. firstly, calculating the linear distance L between the upper anchor point and the lower anchor point of the inhaul cable in the initial state is Then according to the stress-free distance between the upper anchor point and the lower anchor point of the inhaul cable, the cable force F in the initial state is calculated by adopting the following formula s ：
wherein ,L0 Is a stress-free interval;
d. firstly, calculating the straight line distance L between the upper anchor point and the lower anchor point of the inhaul cable in the current state ip According to the stress-free distance between the upper anchor point and the lower anchor point of the inhaul cable and the initial state cable force, calculating the cable force F required by reaching the target state in the current state by adopting the following formula ip ：
wherein ,Fis For the initial state of cable force L is Is the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the initial state, L ip Is the straight line distance between the upper anchor point and the lower anchor point in the current state, L i0 The stress-free distance between the upper anchor point and the lower anchor point of the inhaul cable is not provided.
e. Full displacement constraint is carried out on an upper anchor point and a lower anchor point of a guy cable in the current state, and then the current cable force is replaced and adjusted to F in the form of in-vivo force ip And then, the restraint of the upper anchor point and the lower anchor point is released, and the formed cable force state force is the tensioning force required by the field tensioning of the cable in the current state.
The derivation process of the second cable force calculation method based on the equivalent force displacement method is as follows:
assuming that the total amount of potential energy in the structure is E in the initial state (without the cable structure part) 0 The internal potential energy of the deformation of the structure under the target state (without the cable structure part) is changed into E d The amount of change in the potential energy of the structure (delta Ed ＝E d -E 0 ) Is equal to the total strain energy Sigma U of the inhaul cable when the upper anchor point and the lower anchor point of the inhaul cable are pulled back to the initial state position under the target state is Total strain energy Sigma U of inhaul cable under target state id The difference, delta Ed ＝E d -E 0 ＝∑U is -∑U id 。
Because the potential energy increment from the initial state to the target state of the structure is considered, the actual state potential energy of the structure is not needed to be considered, and the increment that the strain energy is converted into the structure potential energy when the cable force is changed, namely delta, is needed to be considered Ed ＝∑U is -∑U id 。
Under the definition, in the initial structural state of the structure, the total strain energy of the inhaul cable which can enable the structure to reach the target state is as follows:
the total strain energy of the inhaul cable in the target state is as follows:
where i is the number of cords and n is the number of cords.
The calculation formula of the inhaul cable strain energy is as follows:
when F, A is known, ++>
Wherein L is the linear distance between the upper anchor point and the lower anchor point of the stay cable when no stress exists, F is the cable force, E is the elastic modulus (the stay cable is converted into the elastic modulus E considering sagging ernst ) A is the area of the inhaul cable.
Since the cable force in the target state is known, the linear distance L between the upper anchor point and the lower anchor point of the inhaul cable in the target state can be calculated according to the equivalent force model (as shown in the principle of figure 2) d 。
According to the target cable force F d Can calculate the stress-free distance between the upper anchor point and the lower anchor point of the cable as
The straight line distance between the upper anchor point and the lower anchor point of the cable in the initial state is L s The corresponding cable force is F s . Due to L 0 It is known that it is easy to calculate
Therefore, under the initial structural state of the structure, the strain energy of the single inhaul cable which can enable the structure to reach the target state is as follows:
the strain energy corresponding to a single cable in the target state is as follows:
then in the initial state of the structure, the total strain energy difference of the inhaul cable which can enable the structure to reach the target state is as follows:
it can be seen from the above that the strain energy of the single cable is converted into
At a certain stage in one round of cable adjustment, the linear distance L between the current cable anchor points is known ip Straight line distance L between initial cable anchor points is Initial cable force F is Target cable force F id 。
The amount of change in strain energy from the initial state to the current state can be calculated from the decrease in linear distance between the cable anchor points,
namely:
meanwhile, the strain energy difference calculation formula under two different states deduced from the previous can know that the change amount of the strain energy from the initial state to the current state is as follows:
the simultaneous operation can solve the cable force required for reaching the target state from the current state:
F ip the cable force required by the current state to reach the target state is generated by the deformation of the nonlinear structure in the actual tensioning process of the cable force, and new strain energy is converted into structural potential energy, so that the specific actual tensioning force target value is still unknown. Therefore, the full displacement constraint can be carried out on the upper anchor point and the lower anchor point of the current guy cable in the finite element simulation process, and then the current cable force is replaced and adjusted to F ip And then, the restraint of the upper anchor point and the lower anchor point is released, and the formed cable tension state force is the current cable tension target value.
The equal force displacement method can utilize the calculated internal force value (increment) to substitute into 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 an external force, the adjusted cable force is not required to be adjusted again on the premise that the target state of the subsequent batch of adjusted cables is unchanged, namely, all cables of the batch of adjusted cables can reach the target value of the batch of adjusted cables after one normal installation according to the method, the influence of shrinkage creep in the related process can be synchronously considered in the finite element software, namely, the equal shrinkage creep duration effect is considered in the calculation of the equal force target value, and the influence can be counted into the virtual cable force caused by the structural deformation difference.
The two calculation methods can solve the complex and complicated cable adjusting problem, and the required cable tension can be calculated only by defining 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 tension in a staged manner or the final bridge forming target state.
Because the equipotential forces are added in the finite element model conveniently and quickly, the displacement of each node of each stage structure is convenient to check, the complex links in the cable adjusting process can be greatly reduced by applying the method, and the problem of cable adjusting difficulty is effectively solved; compared with the original methods of forward assembly iteration, reverse disassembly and closure and the like, a large amount of process calculation time is saved, the working efficiency is improved, and meanwhile, the structural state of each stage can be checked.
The cable force calculation method based on the equivalent force displacement method is suitable for cable force calculation of a small-deformation cable system structure of a conventional cable-stayed bridge cable force, a tie-bar arch bridge hanging rod cable force and the like.
In this embodiment, a span combination of (64+136+64) m continuous Liang Gongqiao is selected as a specific application case, and the equivalent force displacement method-based cable force calculation method is verified, where the specific application case is as follows:
the bridge adopts a construction mode of 'first girder and then arch and finally suspender', the girder adopts cantilever pouring for construction, the arch rib is erected on the folded girder by adopting a bracket, the suspender is stretched for three times, and the final stretching reaches the target bridge formation state. The boom tensioning sequence and boom force values are shown in table 1.
TABLE 1 boom tensioning sequence and boom force values
When one piece is used, all the hanging rods are stretched by adopting 150kN stretching force, so that the problem of hanging rod stretching force calculation does not exist in one process. In the example, the invention is mainly applied to two and three stages, and in the embodiment, midas/Civil is adopted for modeling calculation, and the specific implementation steps are as follows:
the first step: the initial state analysis before the boom activation is carried out, namely the straight line distance L between the upper anchor point and the lower anchor point of the boom after the arch rib construction is completed is calculated 1 The calculation results are shown in table 2. The initial state of the boom before activation is shown in the principle of fig. 1.
And a second step of: and (5) performing state analysis when the two target hanging rod forces are reached. The two post boom target state forces are known to be 150kN,adding an equivalent load of 150kN into an initial state model before the boom is activated, and calculating the linear distance L between the upper anchor point and the lower anchor point of the boom when the two target boom forces are reached 2 The calculation results are shown in table 2, and the state when the two target hanging rod forces are reached is shown in the principle of fig. 2.
TABLE 2 calculation of the displacement of the upper and lower anchors (unit: mm) for the boom before activation and for the two target states
And a third step of: and (3) performing a post-tensioning state analysis, namely activating the suspenders according to a specified tensioning sequence, and simultaneously applying a tensioning force of 150kN to each suspender in an external force mode while activating each suspender, wherein the calculation result of the internal force of one post-tensioning suspender is shown in the principle of fig. 3.
Fourth step: and (5) calculating the two tensile forces of the boom D1. Before calculation, the state before two boom D1 are defined as the current state. In fact, the analysis of the state before the tensioning of the boom D1 is completed in the third step, so that the linear distance delta between the upper anchor point and the lower anchor point of the boom D1 at the current stage in the state before the tensioning of the boom D1 is changed LD1 (Current) Force F in the current state D1 (Current) Are known, the result query can obtain delta LD1 (Current) ＝2.70mm，F D1 (Current) ＝94.2kN。
Knowing the target state internal force F of the two post-boom D1 D1 (object) From Table 1, the linear distance change delta between the upper and lower anchor points when the boom D1 reaches the two target states is known LD1 (target) =5.06 mm, then the internal force increase required for the boom D1 to reach the two-target state can be calculated as follows.
Calculated F D1 (in vivo force increment required to reach two target forces) ＝173kN。
F is then added to the body in a manner that adds to the force D1 (reaching the two target forces)The required in vivo force increment Substituting the two target states into the model, and calculating to obtain the required tensile force F when the boom D1 reaches the two target states D1 ＝223.6kN。
Fifth step: and (5) calculating two tensile forces of the boom D3. Since the calculation is performed based on the two-piece state of the boom D1 at the time of tensioning the two pieces of boom D3, the two-piece state of the boom D1 is defined as the current state. In the calculation, it is first necessary to determine the two states of the boom D1 and to apply F in a model after one in vitro force D1 The boom D1 is endowed, and the linear distance change delta between the upper anchor point and the lower anchor point of the boom D1 at the current stage under the state before the boom D1 is tensioned can be calculated LD3 (Current) =3.53 mm, current state internal force F D3 (Current) ＝0kN。
Knowing the target state internal force F of the two post-boom D3 D3 (object) From Table 1, the linear distance change delta between the upper and lower anchor points when the boom D3 reaches the two target states is known LD3 (target) =17.91 mm, then the body force increment required by the boom D3 to reach the two target states can be calculated according to the formula in the fourth step. Calculated F D3 (in vivo force increment required to reach two target forces) ＝417kN。
F is then added to the body in a manner that adds to the force D3 (the internal force increment required by reaching the two target forces) is substituted into the model, and the required tension force F when the boom D3 reaches the two target states can be obtained after calculation D3 ＝314.5kN。
Sixth step: the calculation of the two tensioning forces of the suspenders D5, D7, D2, D4 and D6 is sequentially carried out according to the steps, and finally the two target cable forces are achieved after the D6 is tensioned, so that repeated iteration is not needed.
Seventh step: and (5) calculating the tensile force of the three suspenders D1-D7. The three-piece basic calculation process is the same as the two-piece basic calculation process, the initial state is the same as the selection, the target state is equivalent to the three-piece target tension force, and the actual conditions of bridge deck pavement increase, midspan second-stage prestress beam tensioning, side span compression weight removal and the like are considered, so that other tensioning sequences and one-time calculation methods are not different, and are not repeated.
According to the mature and widely applied forward iterative calculation method, the equivalent force displacement method check calculation is carried out, the basic models adopted in the calculation are consistent, the parameter settings are consistent, and the final results are compared as follows:
TABLE 3 comparison of two tension results and forward iteration results
Table 4 comparison of three tension results and forward iteration results
According to comparison of calculation results, the forward-loading iteration method is iterated for a plurality of times enough to basically control the deviation within a small range, the maximum deviation of the bridge formed after one forward loading of the equivalent force displacement calculation method is within 2%, and the standard requirement is met.
According to the tensile force obtained by calculation in the embodiment is basically consistent (in-vitro force), the target state force is basically consistent, and the cable force calculation method based on the equivalent force displacement method is proved to be feasible.
The foregoing examples represent only specific embodiments of the present invention, which are described in more detail and are not to be construed as limiting the scope of the invention. It should be noted that several alternatives, modifications and variations can be made by those skilled in the art without departing from the spirit of the invention, which fall within the scope of the invention. Accordingly, the scope of protection of the present invention is to be determined by the appended claims.
Claims (4)
1. The calculation method is characterized in that the cable force is replaced by an external load in a balanced state, the target state is opposite to the initial state, the upper anchor point and the lower anchor point of the cable are displaced, the linear distance change difference value 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 further the tension force required by on-site tensioning of the cable is 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 cable system structure, and acquiring data of the initial state or the current state and the target state of the cable system structure;
b. calculating the deformation difference delta 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, wherein the inhaul cable force F1 in the current state, the inhaul cable force F2 in the target state and the inhaul cable in the current state L1 Deformation difference delta of linear distance between upper anchor point and lower anchor point of inhaul cable in target state relative to initial state L2 ；
c. Calculating an internal force increment F required by the inhaul cable when the inhaul cable reaches the target state 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;
d. the internal force increment required by the inhaul cable when reaching the target state is replaced by adding the internal force to obtain the cable force after the cable is adjusted in the current state, namely the tension required by field tension;
in the step c, the internal force increment F required by the inhaul cable when the inhaul cable reaches the target state is calculated by adopting the following formula;
wherein ,
wherein L is the linear distance between the upper anchor point and the lower anchor point of the stay cable in the target state, E is the elastic modulus of the stay cable, and when the stay cable is the stay cable, the sag elastic modulus is converted into E ernst A is the cross-sectional area of the inhaul cable, F (virtual Cable force portion)Dividing into two parts Is the variation of the cable force caused by the deformation of the structure caused by nonlinearity in the tensioning process.
2. The method for calculating the cable force based on the equivalent force displacement method according to claim 1, wherein the calculation method substitutes the in-vivo force increment required by the cable when the target state is reached into the finite element software calculation in a mode of adding in-vivo force, and the tension force required by the field tensioning is obtained.
3. 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 an initial state position, balance is maintained, the structural form and an internal force state except the cable are returned to the initial state, the structure is restored to the target state after being released, and the tension force required by on-site tensioning is obtained through the strain energy required by the cable 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 cable system structure, and acquiring data of the initial state or the current state and the target state of the cable system structure;
b. according to the target cable force, the elastic modulus of the cable and the cross section area of the cable, calculating the stress-free distance L between the upper anchor point and the lower anchor point of the cable 0 ；
c. According to the stress-free distance between the upper anchor point and the lower anchor point of the inhaul cable, calculating the cable force F in the initial state s ；
d. According to the change amount of strain energy from the initial state to the current state of the inhaul cable, the stress-free distance between two anchor points of the inhaul cable and the cable force in the initial state, calculating the cable force F required by reaching the target state in the current state ip ；
e. Replacement and adjustment of the cable force in the current state as an in-vivo force ip The formed cable force state force is the tension force required by field tensioning in the current state;
in the step b, firstly, calculating the straight line between the upper anchor point and the lower anchor point of the inhaul cable in the target stateDistance L d Then the stress-free distance L between the upper anchor point and the lower anchor point of the inhaul cable is calculated by adopting the following formula 0 ：
wherein ,Fd For the target cable force, E is the elastic modulus, and the cable is converted into the elastic modulus E considering sagging ernst A is the cross section area of the inhaul cable;
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 L is Then the following formula is adopted to calculate the initial cable force F s ：
wherein ,L0 For stress-free distance, E is the elastic modulus, and the conversion into the elastic modulus E considering sagging when the stay cable is ernst A is the cross section area of the inhaul cable;
in the step d, the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the current state is calculated to be L ip Then the following formula is adopted to calculate the cable force F required by reaching the target state in the current state ip ：
wherein ,Fis For the initial state of cable force L is Is the linear distance between the upper anchor point and the lower anchor point of the inhaul cable in the initial state, L ip Is the straight line distance between the upper anchor point and the lower anchor point in the current state, L i0 The stress-free distance between the upper anchor point and the lower anchor point of the stay cable is that E is the elastic modulus, and the stay cable is converted into the elastic modulus E considering sagging ernst A is the cross section area of the inhaul cable;
at a certain stage in a round of tuning according to energy conservationKnowing the linear distance L between current cable anchor points ip Straight line distance L between initial cable anchor points is Initial cable force F is Target cable force F id ；
The amount of change in strain energy from the initial state to the current state can be calculated from the decrease in linear distance between the cable anchor points,
namely:
the amount of change in strain energy from the initial state to the current state is again:
the rope force F required by reaching the target state from the current state can be solved by combining the two formulas ip Is calculated according to the formula:
4. the cable force calculation method based on the equivalent force displacement method as set forth in claim 3, characterized in that the calculation method performs full displacement constraint on the upper and lower anchor points of the current tensioning cable through finite element analysis software, and then adjusts the current cable force to F in a replacement manner ip And then, the restraint of the upper anchor point and the lower anchor point is released, and the formed cable force state force is the stretching force required by the on-site stretching of the inhaul cable in the current state.
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