A method for solving cable length adjustment amount for adjusting displacement of cable-stayed bridge

Abstract

The application discloses a cable length adjustment amount solving method for adjusting displacement of a cable-stayed bridge, and comprises the following steps: solving an influence matrix of cable length-anchor point displacement; determining a target vector of displacement adjustment; determining an anchor point displacement participation coefficient; and iteratively solving a cable length adjustment value. The application provides a method for stably, conveniently and quickly solving a group of uniform and reasonable cable length adjustment amounts, the cable length correction amounts obtained by the application are uniform and reasonable, and the calculation result is superior to that of a conventional least square method. The iterative method of the application is obviously superior to an existing calculation method, greatly shortens design time consumption, and improves work efficiency. The application can be quickly and accurately used for adjusting the configuration of the cable-stayed bridge, including tower deflection and main beam line shape.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of cable length adjustment of cable-stayed bridges, and particularly relates to a method for solving cable length adjustment amount for adjusting displacement of a cable-stayed bridge. BACKGROUND

[0002] The cable-stayed bridge is a flexible high-order statically indeterminate structure, and adjustment of cable force of the cable-stayed bridge can be abstracted as an optimization solving problem of a group of nonlinear equations. Current solving methods for cable force of the cable-stayed bridge include unconstrained programming solving method, constrained programming solving method, genetic algorithm, neural network method, deep learning method and other methods.

[0003] Chinese patent CN201711178902.4 discloses a cable-supported bridge cable adjustment method based on cable length influence matrix, which comprises the following steps: determining an initial state; tensioning the cables by cable length, calculating an output influence matrix; determining the maximum pull-out amount and the maximum slackening amount allowed for each cable length adjustment; determining the target value, the allowed positive deviation, the negative deviation and the weight coefficient of the control item; determining the optimization objective function according to the required optimization objective; limiting specific constraint conditions according to the optimization objective function of the foregoing steps, obtaining the final value of the cable pull-out amount and the control item and performing cable adjustment. The cable-supported bridge cable adjustment method based on the cable length influence matrix of the invention calculates the cable length influence matrix based on the catenary theory, takes into account the geometric nonlinear effect, and can quickly adjust the cables to the target state.

[0004] However, the invention patent is essentially a constrained optimization method, but only the method for forming the cable length influence matrix, the target function and the constraint condition is given, and the solving method of the optimization equation is not given, which has the following disadvantages: the calculation result is directly determined by the selection of the optimization objective function and the constraint condition, and if the selection is improper, a satisfactory result cannot be obtained, and even an error may occur.

[0005] The paper "Construction control calculation method and application of long-span cable-stayed bridge based on cable length" discloses an overall calculation process and cable adjustment method taking unstressed cable length of the cable as a variable. The cable adjustment calculation meets the cable adjustment target and constraint condition in the order of bridge state, maximum cantilever state and final overall construction stage, and determines the unstressed cable length of each state in sequence; the adjustment value of the adjusted parameters such as main beam line shape, tower deviation and cable force is converted into cable length increment, and iteration is performed in the order of tower deviation, main span main beam line shape and cable force; when the overall geometric shape tends to be stable, the adjusted amount mixed parameter influence matrix is used for auxiliary calculation.

[0006] However, the method converts the adjustment value of the main girder line shape, tower deflection and cable force into cable length increment, and iterates according to the principle of first tower deflection, then main span main girder line shape and finally cable force. The process of iteration is to substitute the adjustment value into the original finite element model. When the iteration number increases and the finite element model is large, this process is extremely time-consuming. For example, if the iteration is 10 times and the finite element model calculation is 10 minutes each time, it needs 100 minutes, and the efficiency is relatively low. Especially in the construction site, since the fine adjustment is mostly carried out at night, the window time is short, and the construction progress may be delayed due to the failure to obtain the construction instruction in time.

[0007] When the overall geometric shape tends to be stable, the adjusted parameter mixed parameter influence matrix is used for auxiliary calculation. This method has the problem that the current influence matrix method may cause uneven cable force.

[0008] In fact, no matter whether it is the constrained influence matrix method, the unconstrained influence matrix method, the mathematical optimization method or the like, the calculation amount is too large, or the cable force obtained is unreasonable and has large jumps, in the actual application process, professional and technical personnel still mostly use the trial method to adjust the cable-stayed cable, which needs to consume more machine time, and the efficiency is relatively low. SUMMARY

[0009] The present application is proposed to solve the problems existing in the prior art, and the purpose is to provide a cable length adjustment amount solving method for adjusting the displacement of a cable-stayed bridge.

[0010] The technical scheme of the present application is: a cable length adjustment amount solving method for adjusting the displacement of a cable-stayed bridge, comprising the following steps:

[0011] First, the influence matrix of cable length-anchor point displacement is solved;

[0012] Then, the target vector of displacement adjustment is determined;

[0013] Then, the anchor point displacement participation coefficient is determined;

[0014] Finally, the cable length adjustment value is iteratively solved.

[0015] Further, the first step of solving the influence matrix of cable length-anchor point displacement specifically includes the following process:

[0016] First, a one-time bridge finite element simulation model of the cable-stayed bridge is established;

[0017] Then, the unstressed cable length of the i-th cable-stayed cable is changed in turn e ;

[0018] Then, the vertical displacement change B of the j-th beam end anchor point ij , and the longitudinal displacement change C of the j-th tower end anchor point are extractedij ;

[0019] Finally, the cable length-beam end anchor point vertical displacement influence matrix B and the cable length-pylon end anchor point influence matrix C are formed respectively, and the specific process is as follows:

[0020] .

[0021] Further, the cable is simulated by using a catenary element, the cable length is negative for shortening and positive for elongation; the displacement is positive for upward and negative for downward; the tower deflection is positive for large mileage and negative for small mileage.

[0022] Further, the second step determines the target vector of displacement adjustment, including determining the target vector of displacement adjustment of the beam end anchor point, which specifically includes the following process:

[0023] Suppose that the whole bridge has n pairs / roots of independent cables, let the target elevation of the beam end anchor point corresponding to the ith pair / root of cable be H ki , the initial elevation of the beam end anchor point of the ith pair / root of cable be H ci , and the vertical displacement of the beam end anchor point that needs to be adjusted be D bi =H ki -H ci , and the vertical displacement increment vector of the beam end anchor point corresponding to the n pairs / roots of cables of the whole bridge that needs to be adjusted be D b =(D bi )i=1~n.

[0024] Further, the second step determines the target vector of displacement adjustment, including determining the target vector of displacement adjustment of the bridge tower anchor point, which specifically includes the following process:

[0025] Let the target tower deflection of the tower end anchor point corresponding to the ith pair / root of cable be I ki , the initial tower deflection of the tower end anchor point be I ci , the longitudinal displacement of the tower end anchor point that needs to be adjusted be D ti =I ki -I ci , and the longitudinal displacement increment vector of the tower end anchor point corresponding to the n pairs / roots of cables of the whole bridge that needs to be adjusted be D t =(D ti )i=1~n.

[0026] Further, the third step determines the anchor point displacement participation coefficient, which determines whether the displacement of each beam end anchor point and tower end anchor point participates in the correction of the cable length and the degree of participation, including solving the displacement correction participation coefficient of the beam end anchor point and solving the displacement correction participation coefficient of the tower end anchor point.

[0027] Further, the displacement correction participation coefficient of the beam end anchor point is solved, which specifically includes the following process:

[0028] Let δ bi be the displacement correction participation factor of the i-th cable beam end anchor point, which can be taken as 0~1.2, for the cable with small stiffness compared with the beam, such as 1~2 pairs per cable near the tower, the concrete side span cable of hybrid girder cable-stayed bridge, the anchoring cable near the support, the cable which is not expected to adjust the cable length, etc. The value of the beam end anchor point corresponding to these cables can be taken as 0, and the value of the cable other than the above-mentioned cases is taken as 1.0 or 1.2.

[0029] Further, the displacement correction participation factor of the tower end anchor point is solved, which specifically includes the following process:

[0030] Let δ ti be the displacement correction participation factor of the i-th cable tower end anchor point, which can be taken as 0~1.2, for the cable with small stiffness compared with the tower, such as the mid-span cable, other non-anchoring cable, cable which is not expected to adjust the cable length, etc. The value of the tower end anchor point corresponding to these cables can be taken as 0, and the value of the cable other than the above-mentioned cases, especially the anchoring cable near the support or the concrete side span cable of hybrid girder cable-stayed bridge, is taken as 1.0 or 1.2.

[0031] Further, the fourth step is to iteratively solve the cable length adjustment value, and the adjustment of the cable is carried out in the order of first iteratively adjusting the main beam displacement and then adjusting the main tower displacement.

[0032] Further, the iterative solution of the cable length adjustment value specifically includes the following process:

[0033] Let L k+1 be the cable length cumulative correction value calculated in the k+1th iteration, L k be the cable length cumulative correction value calculated in the kth iteration, L' k be the cable length correction increment calculated in the kth iteration, c bk be the allowable error of the main beam anchor point displacement of the cable-stayed bridge, c tk be the allowable error of the main tower anchor point displacement of the cable-stayed bridge;

[0034] L0=0,

[0035] L k+1 = L k +L' k

[0036] When max(abs(c b )) ≥c bk , L' k =-(D b -[B]L k )(δ b )sin α

[0037] When max(abs(c) b )) <c bk And max(abs(c t ))≥c tk At that time, L′ k =(D t -[C]L k )(δ t cos α

[0038] When max(abs(c) b )) <c bk And max(abs(c) t )) <c tk End iteration.

[0039] in,

[0040] c b =(D b -[B]L k )m b

[0041] c t =(D t -[B]L k )m t

[0042] m b and m t This is a switch that controls whether the displacement at the anchor point is controlled. When the value is set to 0, the displacement at this position is not controlled; when the value is set to 1, the displacement at this position is controlled.

[0043] α Let α be the spatial angle between the cable and the horizontal plane, satisfying 0 < α < 180°.

[0044] This invention provides a stable, convenient, and fast method for solving a set of uniform and reasonable cable length adjustment amounts. The cable length correction amounts obtained by this invention are uniform and reasonable, and the calculation results are better than the conventional least squares method. The iterative method of this invention is significantly better than the existing calculation methods, greatly shortening the design time and improving work efficiency. Attached Figure Description

[0045] Figure 1 This is a bridge layout diagram of the double-tower, double-cable-stayed hybrid beam cable-stayed bridge in this invention;

[0046] Figure 2 The initial cable force is determined by the load balance method in this embodiment of the invention;

[0047] Figure 3is the comparison between the initial cable force and the target cable force in the design optimization;

[0048] Figure 4 is the cable length correction value of the cable-stayed bridge calculated by the method of the present application in the design optimization;

[0049] Figure 5 is the comparison between the initial cable force and the optimized cable force calculated by the method of the present application in the design optimization;

[0050] Figure 6 is the comparison between the initial cable force and the optimized cable force calculated by the method of the present application in the design optimization;

[0051] Figure 7 is the comparison between the initial cable force and the optimized cable force calculated by the method of the present application in the design optimization;

[0052] Figure 8 is the cable length correction value of the cable-stayed bridge calculated by the method of the present application in the design optimization;

[0053] Figure 9 is the comparison between the initial cable force and the optimized cable force calculated by the method of the present application in the design optimization;

[0054] Figure 10 is the comparison between the initial cable force and the optimized cable force calculated by the method of the present application in the design optimization;

[0055] Figure 11 is the cable length correction value of the cable-stayed bridge calculated by the method of the present application in the design optimization;

[0056] Figure 12 is the final cable force value calculated by the method of the present application in the design optimization;

[0057] Figure 13 is the cable length correction value of the cable-stayed bridge calculated by the method of the present application in the design optimization;

[0058] Figure 14 is the final cable force value calculated by the method of the present application in the design optimization;

[0059] Figure 15 is the displacement error convergence curve calculated by the method of the present application. DETAILED DESCRIPTION

[0060] Hereinafter, the present application will be described in detail with reference to the accompanying drawings and examples:

[0061] As shown in Figures 1-13 , a cable length adjustment amount solving method for adjusting the displacement of a cable-stayed bridge, comprising the following steps:

[0062] First, the influence matrix of cable length-anchorage point displacement is solved;

[0063] Then, the target vector of displacement adjustment is determined;

[0064] Further, the anchor point displacement participation coefficient is determined;

[0065] Finally, the cable length adjustment value is iteratively solved.

[0066] Further, the first step is to solve the influence matrix of cable length-anchor point displacement, which specifically includes the following process:

[0067] Firstly, a finite element simulation model of the cable-stayed bridge is established;

[0068] Then, the unstressed cable length of the i-th cable is changed in turn e ;

[0069] Further, the vertical displacement change B ij of the j-th beam end anchor point and the longitudinal displacement change C ij of the j-th tower end anchor point are extracted;

[0070] Finally, the cable length-beam end anchor point vertical displacement influence matrix B and the cable length-tower end anchor point influence matrix C are formed respectively, which are as follows:

[0071] .

[0072] Further, the cable-stayed cable is simulated by catenary element, the cable length of the cable-stayed cable is negative for shortening and positive for elongation; the displacement is positive for upward and negative for downward; the tower deviation is positive for large mileage and negative for small mileage.

[0073] Further, the second step is to determine the target vector of displacement adjustment, which includes determining the target vector of beam end anchor point displacement adjustment, which specifically includes the following process:

[0074] Suppose that there are n pairs / roots of independent cable-stayed cables in the whole bridge, let the target elevation of the beam end anchor point corresponding to the i-th pair / root of cable-stayed cable be H ki , the initial elevation of the beam end anchor point of the i-th pair / root of cable-stayed cable be H ci , the vertical displacement of the beam end anchor point that needs to be adjusted be D bi = H ki -H ci , and the vertical displacement increment vector of the beam end anchor point corresponding to the n pairs / roots of cable-stayed cables in the whole bridge that needs to be adjusted be D b = (D bi )i=1~n.

[0075] Further, the second step is to determine the target vector of displacement adjustment, which includes determining the target vector of bridge tower anchor point displacement adjustment, which specifically includes the following process:

[0076] Let the target tower deviation of the tower end anchor point corresponding to the i-th pair / root of cable-stayed cable be I ki, the initial tower anchor point initial tower deviation is I ci , the tower anchor point longitudinal displacement that needs to be adjusted is D ti =I ki -I ci , the tower anchor point longitudinal displacement increment vector that needs to be adjusted corresponding to the full-bridge n pairs of cable-stayed cables is D t =(D ti )i=1~n.

[0077] Further, the third step determines the anchor point displacement participation coefficient, determines whether the displacement of each beam end anchor point and tower anchor point participates in the correction of the cable length and the participation degree, including solving the displacement correction participation coefficient of the beam end anchor point, and solving the displacement correction participation coefficient of the tower anchor point.

[0078] Further, the displacement correction participation coefficient of the beam end anchor point is solved, which specifically includes the following process:

[0079] Let δ bi be the displacement correction participation coefficient of the beam end anchor point of the i-th cable-stayed cable, which can be taken as 0-1.2. For cable-stayed cables with small beam stiffness, such as 1-2 pairs of cables per root near the tower root, concrete side span cables of hybrid girder cable-stayed bridges, anchor cables near the support, and cable-stayed cables that do not need to adjust the cable length, the value of the beam end anchor point corresponding to these cable-stayed cables can be taken as 0, and the value of the cable-stayed cables other than the above-mentioned cases is taken as 1.0 or 1.2.

[0080] Further, the displacement correction participation coefficient of the tower anchor point is solved, which specifically includes the following process:

[0081] Let δ ti be the displacement correction participation coefficient of the tower anchor point of the i-th cable-stayed cable, which can be taken as 0-1.2. For cable-stayed cables with small tower stiffness, such as mid-span cable-stayed cables, other non-anchor cables, and cable-stayed cables that do not need to adjust the cable length, the value of the tower anchor point corresponding to these cable-stayed cables can be taken as 0, and the value of the cable-stayed cables other than the above-mentioned cases, especially the anchor cables near the support or the concrete side span cables of hybrid girder cable-stayed bridges, is taken as 1.0 or 1.2.

[0082] Further, the fourth step iteratively solves the cable length adjustment value, and adjusts the cable-stayed cable in the order of first iteratively adjusting the main beam displacement and then adjusting the main tower displacement.

[0083] Further, the cable length adjustment value is iteratively solved, which specifically includes the following process:

[0084] Let L k+1 be the cable length cumulative correction value calculated in the k+1th iteration, L k be the cable length cumulative correction value calculated in the kth iteration, L' k be the cable length correction increment calculated in the kth iteration, cbk is the displacement allowable error of the main girder anchor point of the cable-stayed bridge, tk is the displacement allowable error of the main tower anchor point of the cable-stayed bridge;

[0085] L0=0,

[0086] L k+1 = L k +L′ k

[0087] When max(abs(c b )) ≥c bk , L′ k =-(D b -[B]L k )(δ b )sin α

[0088] When max(abs(c b ))<c bk , and max(abs(c t ))≥c tk , L′ k =(D t -[C]L k )(δ t )cos α

[0089] When max(abs(c b ))<c bk , and max(abs(c t )) <c tk , end iteration,

[0090] wherein,

[0091] c b =(D b -[B]L k )m b

[0092] c t =(D t -[B]L k )m t

[0093] m b and m t are switches for whether the displacement at the anchor point is controlled, when the value is set to 0, the displacement at the position is not controlled, and when the value is set to 1, the displacement at the position is controlled;

[0094] α is the spatial included angle between the cable-stayed cable and the horizontal plane, satisfying 0<α<180°. Example

[0095] The following description, in conjunction with specific embodiments, illustrates the process.

[0096] The bridge is a (67.5+60+60+350+60+60+67.5)m double-tower, double-cable-stayed hybrid beam bridge. The side spans are prestressed concrete box girders with a height of 4.5m, while the middle span is a steel-concrete composite beam with a height of 4.5m. The bridge is designed for a speed of 350km / h and uses vibration-damping ballastless track. The steel-concrete composite section is located 21m from the center of the bridge towers in the middle span of the main beam. Eighteen pairs of stay cables are installed on each side of the main towers, arranged in a fan shape, with a cable spacing of 9m on the main beam. The main towers are constructed of C50 reinforced concrete and are 109m high above the bridge deck.

[0097] Application in the design optimization of cable-stayed bridges

[0098] a. Preliminary estimation of cable forces in a cable-stayed bridge using the load balance method.

[0099] The load balance method assumes that each pair of stay cables bears the weight of the main beam within its own range.

[0100] ;

[0101] In the formula, Q is the weight of the main beam near the stay cable (including the secondary dead load).

[0102] θ — Inclination angle of the cable.

[0103] The initial cable forces of the stay cables, assumed according to the load balance method, are shown in the table below:

[0104]

[0105] b. Calculate the initial stress-free cable length using the catenary formula.

[0106] The method for calculating the stress-free cable length of a cable-stayed bridge using the catenary formula can be obtained from currently available literature, and will not be elaborated in detail in this application. The calculated initial stress-free cable lengths for this bridge corresponding to the aforementioned preliminary cable forces are shown in the table below:

[0107]

[0108] c. Establish a finite element model of the bridge constructed in one phase using the aforementioned initial stress-free cable length.

[0109] The finite element model of the bridge was established using commonly used finite element software in the field of cable-stayed bridge calculation technology, such as Midas Civil and Nlabs. The stress-free cable lengths of the cable stays are as shown in the table above.

[0110] d. Calculate the influence matrix of cable length-anchor point displacement.

[0111] On the basis of the above model, the cable length-anchorage displacement influence matrix is solved by changing the length of each cable / pair of cables. Due to the large size of the influence matrix, the influence matrix is not specifically described.

[0112] e. A finite element model considering the construction stage is established, or the above one-time bridge finite element model is directly used for calculation to obtain the cable-stayed bridge tower deflection and main girder alignment corresponding to the current unstressed cable length.

[0113] f. The target alignment of the zero displacement method is taken as the target vector of the adjustment of the anchorage displacement of the beam end.

[0114] Suppose there are n pairs of (roots) of independent cables in the whole bridge, and let the target elevation of the beam end anchorage corresponding to the i-th cable be H ki , the initial elevation of the beam end anchorage of the i-th cable at present be H ci , and the vertical displacement of the beam end anchorage that needs to be adjusted be D bi = H ki -H ci The vertical displacement increment vector of the beam end anchorage of the n pairs (roots) of cables in the whole bridge that needs to be adjusted is D b = (D bi )i=1~n.

[0115] Taking this bridge as an example, the displacement adjustment target vector of the anchorage of the beam end is shown in the following table:

[0116]

[0117] g. Determine the anchorage displacement participation coefficient of the main girder

[0118] Let δ bi be the displacement correction participation coefficient of the anchorage of the i-th cable at the beam end. This value can be taken as 0~1.2. For cables with a small cable-girder stiffness ratio, such as 1~2 pairs (roots) of cables near the tower root, concrete side span cables of hybrid girder cable-stayed bridges, anchorage cables near the support, and cables that do not need to be adjusted in length, the value of the anchorage of the beam end corresponding to these cables can be taken as 0. For cables other than the above, the value can be taken as 1.0 or 1.2.

[0119] In this example, the displacement participation coefficients of the S1 and M1 cables near the tower root are set to 0, and the displacement participation coefficients of the anchorage of the beam end are all set to 1.0.

[0120] h. Determine the coefficient m of whether the displacement of the main girder participates in the control b

[0121] For this bridge, the displacements of the S1 and M1 cables near the tower root do not participate in the error control calculation, i.e. m b= 0 to avoid abnormal solution. The m b coefficient of other cable-stayed cables is set to 1.

[0122] i. Determine the target vector of the displacement adjustment of the tower anchor point

[0123] Let the target tower deflection of the tower end anchor point corresponding to the ith cable-stayed cable be I ki , and the initial tower deflection of the tower end anchor point be I ci , then the longitudinal displacement of the tower end anchor point that needs to be adjusted is D ti = I ki -I ci The longitudinal displacement increment vector of the tower end anchor point corresponding to the n pairs (roots) of cable-stayed cables of the whole bridge that needs to be adjusted is D t = (D ti ) i = 1 ~ n.

[0124]

[0125] j. Determine the anchor point displacement participation coefficient of the main tower

[0126] Let δ ti be the displacement correction participation coefficient of the tower end anchor point of the ith cable-stayed cable. The value can be taken as 0 ~ 1.2. For cable-stayed cables with small tower stiffness, such as mid-span cable-stayed cables, other non-anchored cables, cable-stayed cables that do not want to adjust the cable length, etc., the value of the tower end anchor point corresponding to these cable-stayed cables can be taken as 0, and for cable-stayed cables other than the above-mentioned cases, especially anchor cables near the support or concrete side span cables of hybrid girder cable-stayed bridges, the value can be taken as 1.0 or 1.2.

[0127] In this example, the displacement participation coefficient of S1 and M1 short cables near the tower root is set to 0, and the displacement participation coefficient of other tower end anchor points is set to 1.0.

[0128] k. Determine the coefficient m of whether the displacement of the main tower participates in the control t

[0129] For this bridge, the cable-stayed cable displacement of S1 and M1 two cables near the tower root is not involved in the error control calculation, that is, the m t of these two cables is set to 0 to avoid abnormal solution. The m t coefficient of other cable-stayed cables is set to 1.

[0130] l. Determine the angle of the cable-stayed cable of the bridge

[0131] The angle of the cable-stayed cable in this example is shown in the following table:

[0132]

[0133] m. Iterative solution of cable length adjustment value

[0134] The adjustment of the stay cable is performed in the order of first adjusting the displacement of the main beam and then adjusting the displacement of the main tower.

[0135] Let L k+1 be the cumulative correction value of the cable length calculated in the k+1th iteration, L k be the cumulative correction value of the cable length calculated in the kth iteration, L' k be the correction increment of the cable length calculated in the kth iteration, c bk be the allowable error of the displacement of the main beam anchor point of the cable-stayed bridge, c tk be the allowable error of the displacement of the main tower anchor point of the cable-stayed bridge.

[0136] L0=0,

[0137] L k+1 = L k +L' k

[0138] When max(abs(c b )) ≥c bk , L' k =-(D b -[B]L k )(δ b )sin α

[0139] When max(abs(c b ))<c bk , and max(abs(c t ))≥c bk , L' k =(D t -[C]L k )(δ t )cos α

[0140] When max(abs(c b ))<c bk , and max(abs(c t )) <c bk , the iteration is ended.

[0141] wherein,

[0142] c b =(D b -[B]L k )m b

[0143] c t =(D t -[B]L k )m t

[0144] The displacement limit difference c of the example is set bk =5mm, c tk =10mm, and the maximum iteration number is 50.

[0145] The calculation result is calculated as follows:

[0146]

[0147] As can be seen from the embodiment, the method provided by the application can quickly and conveniently perform the optimization calculation of the linear shape of the main girder of the cable-stayed bridge, and obvious effects are achieved.

[0148] Application in cable-stayed bridge construction control

[0149] In the field of cable-stayed bridge construction control, after the closure of the cable-stayed bridge, the bridge deck linear shape needs to be adjusted to the target linear shape through overall cable adjustment, and the method of the application can be used to achieve the same.

[0150] Problem description: after the closure of the cable-stayed bridge, the main girder linear shape needs to be adjusted to the 0.5‰ herringbone form, and the tower deviation is unchanged.

[0151] i. Calculate the influence matrix of cable length-anchor point displacement

[0152] On the basis of the once-bridge model, the unit cable length of each (pair) cable is changed, and the cable length-anchor point displacement influence matrix is solved. Since the influence matrix is large in size, the influence matrix is not shown.

[0153] ii. Determine the target vector of the adjustment of the beam end anchor point displacement according to the difference between the target linear shape and the initial linear shape

[0154] Suppose that the whole bridge has n pairs (roots) of independent cable-stayed cables, let the target elevation of the beam end anchor point corresponding to the i-th cable-stayed cable be H ki , the initial elevation of the beam end anchor point of the i-th cable-stayed cable be H ci , and the vertical displacement of the beam end anchor point to be adjusted be D bi =H ki -H ci , and the vertical displacement increment vector of the beam end anchor point of the whole bridge n pairs (roots) of cable-stayed cables to be adjusted be D b =(D bi )i=1~n.

[0155] Taking the bridge as an example, the displacement adjustment target vector of the beam end anchor point is shown in the following table:

[0156]

[0157] iii. Determine the anchor point displacement participation coefficient of the main girder

[0158] Let δ biis the displacement correction participation coefficient of the i-th cable beam end anchor point, which can be taken as 0~1.2. For the cable with small stiffness ratio, such as 1~2 pairs (roots) of cables near the tower root, the concrete side span cable of the hybrid girder cable-stayed bridge, the anchoring cable near the support, and the cable that is not expected to adjust the cable length, the value of the beam end anchor point corresponding to the cable can be taken as 0. For the cable other than the above-mentioned cases, the value can be taken as 1.0 or 1.2.

[0159] In this example, the displacement participation coefficients of S1 and M1 cables near the tower root are set to 0, and the displacement participation coefficients of other beam end anchors are all set to 1.0.

[0160] ⅳ. Determine the coefficient m of whether the displacement of the main girder participates in the control b

[0161] For this bridge, the displacements of S1, S2, S3 and M1, M2, M3 cables near the tower root do not participate in the error control calculation, that is, the m b coefficients of the two cables are set to 0 to avoid abnormal solution. The m b coefficients of other cables are all set to 1.

[0162] ⅴ. Determine the target vector of the displacement adjustment of the tower anchor point

[0163] Let the target tower deflection of the tower end anchor point corresponding to the i-th cable be I ki , the initial tower deflection of the tower end anchor point be I ci , and the longitudinal displacement of the tower end anchor point that needs to be adjusted be D ti =I ki -I ci . The longitudinal displacement increment vector of the tower end anchor point corresponding to the n pairs (roots) of cables of the whole bridge that needs to be adjusted is D t =(D ti )i=1~n.

[0164]

[0165] ⅵ. Determine the anchor point displacement participation coefficient of the main tower

[0166] Let δ ti be the displacement correction participation coefficient of the i-th cable tower end anchor point. The value can be taken as 0~1.2. For the cable with small tower stiffness, such as the mid-span cable, other non-anchoring cable, and cable that is not expected to adjust the cable length, the value of the tower end anchor point corresponding to the cable can be taken as 0. For the cable other than the above-mentioned cases, especially the anchoring cable near the support or the concrete side span cable of the hybrid girder cable-stayed bridge, the value can be taken as 1.0 or 1.2.

[0167] In this example, the displacement participation factor for the short cables S1 and M1 near the tower root is set to 0, while the displacement participation factor for other tower end anchor points is set to 1.0.

[0168] vii. Determine whether the displacement of the main tower is included in the control coefficient m. t

[0169] For this bridge, the displacements of the stay cables S1, S2, S3 and M1, M2, M3 near the tower base are not included in the error control calculation. That is, the displacements of these stay cables (m...) t =0, to avoid distorted solutions. The m values ​​for other stay cables are... t All coefficients are set to 1.

[0170] ⅷ. Determine the angle of the bridge's stay cables.

[0171] The angles of the stay cables in this example are shown in the table below:

[0172]

[0173] ⅸ. Iteratively solve for the cable length adjustment value

[0174] The stay cables are adjusted in the following order: first, the displacement of the main beam is adjusted iteratively, and then the displacement of the main tower is adjusted.

[0175] Let L k+1 L is the cumulative correction value of the cable length calculated in the (k+1)th iteration. k L′ is the cumulative correction value of the cable length calculated in the k-th iteration. k c is the cable length correction increment calculated in the k-th iteration. bk c represents the allowable error for the displacement of the anchor points of the main girder of a cable-stayed bridge. tk This refers to the allowable error for the displacement of the anchor points of the main tower of a cable-stayed bridge.

[0176] L0=0,

[0177] L k+1 = L k +L′ k

[0178] When max(abs(c) b )) ≥c bk At that time, L′ k =-(D b -[B]L k )(δ b sin α

[0179] When max(abs(c) b )) <c bk And max(abs(c t ))≥c tkL' k = (D t -[C]L k )(δ t )cos α

[0180] When max(abs(c b )) <c bk and max(abs(c t )) <c tk , end iteration.

[0181] Wherein,

[0182] c b = (D b -[B]L k )m b

[0183] c t = (D t -[B]L k )m t

[0184] In this example, the displacement tolerance c bk = 5mm, c tk = 10mm, and the maximum number of iterations is 50.

[0185] The calculation results are as follows:

[0186]

[0187] As a comparison, the linear shape corresponding to the initial cable force in the design optimization is compared with the target linear shape.

[0188] The cable length adjustment amount of the cable-stayed cable is calculated by using the least square method and the method proposed in the application respectively, and the calculation results are compared to obtain the following comparison data:

[0189] Figure 11 is the cable length correction value of the cable-stayed cable calculated by using the least square method;

[0190] Figure 12 is the final cable force value calculated by using the least square method;

[0191] Figure 13 is the cable length correction value of the cable-stayed cable calculated by using the method of the application;

[0192] Figure 14 is the final cable force value calculated by using the method of the application;

[0193] Comparison Figure 11 and Figure 13It can be known that the cable length correction value calculated by the least square method reaches-2.14m~5.15m, and the jump is uneven, which is obviously unreasonable; the cable length correction value calculated by the method of the application is-0.14m~0.03m, and the cable length correction is relatively uniform.

[0194] Comparison Figure 12 and Figure 14 It can be known that the final cable force value calculated by the least square method is-74285kN~31935kN, and even a pressure value appears, which is obviously unreasonable; the final cable force value calculated by the application is 2694kN~4703kN, and the cable force is also relatively uniform. Therefore, the result calculated by the method of the application is better than the conventional least square method.

[0195] Comparison with the trial method

[0196] In terms of efficiency, the iteration method is used to calculate the application, the convergence precision is set to 0.005m, and a total of 15 iterations are performed, and through statistics, the total time is 0.8s. The convergence curve is as shown in Figure 15 .

[0197] The method introduced in the document "Construction control calculation method and application of long-span cable-stayed bridge based on cable length" is used, and 300s is needed for each iteration calculation, and 4500s is needed for 15 iterations, so the efficiency of the method of the application is obviously better than that in the document "Construction control calculation method and application of long-span cable-stayed bridge based on cable length".

[0198] The application provides a stable, convenient and fast method for solving a group of uniform and reasonable cable length adjustment values. The cable length correction value obtained by the application is uniform and reasonable, the calculation result is better than the conventional least square method, the iteration method of the application is obviously better than the existing calculation method, the design time is greatly shortened, and the work efficiency is improved.

Claims

1. A method for determining the cable length adjustment amount for adjusting the displacement of a cable-stayed bridge, characterized in that: Includes the following steps: First, solve the influence matrix of cable length-anchor point displacement to form the influence matrix B of cable length-beam end anchor point vertical displacement and the influence matrix C of cable length-tower end anchor point. Then, determine the target vector for displacement adjustment; The target vector includes the vertical displacement increment vector that needs to be adjusted for the beam end anchor points corresponding to n pairs / lengths of stay cables across the entire bridge, denoted as D. b =(D bi i = 1 ~ n; The target vector also includes the longitudinal displacement increment vector D corresponding to the tower end anchor points of the n pairs / lengths of stay cables for the entire bridge. t =(D ti i = 1 ~ n; Next, determine the anchor point displacement participation factor; For each beam end anchor point and tower end anchor point, determine whether the displacement participates in the cable length correction and the degree of participation, including solving the displacement correction participation coefficient of the beam end anchor point and the displacement correction participation coefficient of the tower end anchor point; Let δ bi The displacement correction participation factor for the anchor point at the end of the i-th cable-stayed beam is 0~1.

2. Let δ ti The displacement correction participation factor for the anchor point at the end of the i-th cable-stayed tower is 0 to 1.

2. Finally, the cable length adjustment value is solved iteratively; Let L k+1 L is the cumulative correction value of the cable length calculated in the (k+1)th iteration. k L′ is the cumulative correction value of the cable length calculated in the k-th iteration. k c is the cable length correction increment calculated in the k-th iteration. bk c represents the allowable error for the displacement of the anchor points of the main girder of a cable-stayed bridge. tk This refers to the allowable error for the displacement of the anchor points of the main tower of a cable-stayed bridge. L0=0， L k+1 = L k +L′ k When max(abs(c) b )) ≥c bk At that time, L′ k =-(D b -[B]L k )(δ b sin α When max(abs(c) b )) <c bk And max(abs(c t ))≥c tk At that time, L′ k =(D t -[C]L k )(δ t cos α When max(abs(c) b )) <c bk And max(abs(c) t )) <c tk End iteration. in, c b =(D b -[B]L k )m b c t =(D t -[B]L k )m t m b and m t This is a switch that controls whether the displacement at the anchor point is controlled. When the value is set to 0, the displacement at this position is not controlled; when the value is set to 1, the displacement at this position is controlled. α Let α be the spatial angle between the cable and the horizontal plane, satisfying 0 < α < 180°.

2. The method for calculating the cable length adjustment amount for adjusting the displacement of a cable-stayed bridge according to claim 1, characterized in that: The first step is to solve the influence matrix of cable length-anchor point displacement, which includes the following steps: First, a finite element simulation model of the cable-stayed bridge is established for a single completed bridge; Then, the stress-free cable length of the i-th cable is changed sequentially. e ; Next, extract the vertical displacement change B at the j-th beam end anchor point. ij And the longitudinal displacement change C of the j-th tower end anchor point ij ; Finally, the influence matrix B of cable length-beam end anchor point vertical displacement and the influence matrix C of cable length-tower end anchor point are respectively formed, as follows: 。 3. The method for calculating the cable length adjustment amount for adjusting the displacement of a cable-stayed bridge according to claim 2, characterized in that: The stay cables are simulated using catenary elements. The cable length is negative when shortening and positive when elongating; the displacement is positive when upward and negative when downward; the tower deflection is positive when the distance to the tower is greater and negative when the distance to the tower is less.

4. The method for calculating the cable length adjustment amount for adjusting the displacement of a cable-stayed bridge according to claim 1, characterized in that: The second step is to determine the target vector for displacement adjustment, including determining the target vector for beam end anchor point displacement adjustment, which specifically includes the following process: Suppose the bridge has n pairs / individual stay cables, and let H be the target elevation of the beam end anchor point corresponding to the i-th pair / individual stay cable. ki The initial elevation of the current beam end anchor point of the i-th pair / staying cable is H. ci The vertical displacement of the beam end anchor point that needs to be adjusted is D. bi =H ki -H ci The vertical displacement increment vector that needs to be adjusted for the beam end anchor points corresponding to n pairs / lengths of stay cables for the entire bridge is D. b =(D bi i = 1 ~ n.

5. The method for calculating the cable length adjustment amount for adjusting the displacement of a cable-stayed bridge according to claim 4, characterized in that: The second step is to determine the target vector for displacement adjustment, including determining the target vector for bridge tower anchor point displacement adjustment, which specifically includes the following process: Let the target tower offset of the tower end anchor point corresponding to the i-th pair / strand stay cable be I. ki The initial tower offset at the tower end anchor point is I. ci The required longitudinal displacement of the tower end anchor point is D. ti =I ki -I ci The longitudinal displacement increment vector that needs to be adjusted for the tower end anchor points corresponding to n pairs / lengths of stay cables for the entire bridge is D. t =(D ti i = 1 ~ n.

6. The method for calculating the cable length adjustment amount for adjusting the displacement of a cable-stayed bridge according to claim 1, characterized in that: The fourth step involves iteratively solving for the cable length adjustment value, adjusting the stay cables in the order of first iteratively adjusting the main beam displacement, and then adjusting the main tower displacement.

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