Optimization Method for External Stay Cables, Internal Prestressing Tendons and Bridge Towers of Low Tower Cable-Stayed Bridges

Abstract

The present invention relates to the technical field of construction engineering, and provides an optimization method for external stay cables, internal prestressing tendons and bridge towers of a low tower cable-stayed bridge, including: S1. Regarding the cable force, prestress and tower height as variables to be optimized at the same time, deriving the formula for their collaborative optimization, and solving the optimization problem with the help of programming language; S2. Calculating the influence of the unit cable force of a single stay cable on the stresses of the upper and lower edges of the main girder, and obtaining the influence matrix of the cable force after linear superposition. Similarly, obtaining the influence matrix of the prestressed steel bars on the top and bottom plates of the main girder; S3. Taking the concrete stress of the main girder meeting the specification requirements as the constraint condition of the optimization problem, and incorporating the constraint condition into the optimization objective function by the penalty function method; S4. Establishing the functional relationship between the variables to be optimized and the cost, and obtaining the values of the optimized variables corresponding to the minimum cost of the tower, cables and tendons through the optimization algorithm; S5. Solving the optimization problem multiple times, and statistically obtaining the uniform optimization result of the multi-valued function according to the law of large numbers. The present invention can comprehensively optimize the design of a low tower cable-stayed bridge.

Description

Technical Field

[0001] The present invention relates to the technical field of construction engineering, and more specifically, to an optimization method for external stay cables, internal prestressing tendons and bridge towers of a low tower cable-stayed bridge. Background Art

[0002] A low tower cable-stayed bridge is a cable-beam composite system structure, in which the internal prestress and the stay cables serving as external prestress jointly resist the bending moment of the main girder caused by external loads.

[0003] In design practice, usually the tower height, the layout of stay cables and the cable forces are first determined according to experience, and the remaining bending moment of the main girder is borne by the internal prestress. The distribution of the external load bending moment between the internal prestress and the external stay cables in this method is determined according to experience, and it is difficult to achieve the best matching of the internal prestress and the external stay cables. Some scholars have studied the optimization method of internal prestress and external cables based on the principle of minimum cost, but in this method, the tower height is a determined value, that is, the eccentricity of the external cable cannot be adjusted, and the analytical formula for the optimal cable force needs to be deduced, which needs to be re-deduced according to different specific designs and is not convenient for practical application in engineering.

[0004] Currently, most of the research on the cable force optimization of low tower cable-stayed bridges still optimizes the external cable force and the internal prestress separately, and there is no relevant research on optimizing the external cable force, the internal prestress and the tower height simultaneously.

[0005] Compared with the following existing technologies, the following problems exist:

[0006] (1) Some scholars have studied the secondary optimization method for the cable force of a low tower cable-stayed bridge based on the influence matrix: Based on the principle of the influence matrix, with the minimum overall bending energy of the structure as the goal and the bending moment and displacement as the constraint conditions, the preliminary optimized cable force is obtained, and then with the ideal cable force at the completed bridge as the control goal, the forward iteration calculation is carried out by the linear interpolation method to obtain the second optimized cable force.

[0007] Disadvantages: This method still optimizes the cable force of a low tower cable-stayed bridge by using the influence matrix method, which is more suitable for the cable force optimization of cable-stayed bridges, and fails to consider the influence of the bending moment borne by the main girder on the cable force.

[0008] (2) Some scholars have further improved on the basis of the particle swarm algorithm and developed an optimization method for the cable force of a low tower cable-stayed bridge based on the quantum particle swarm algorithm.

[0009] Disadvantages: The variable selection in this method is only the cable force, ignoring the influence of the internal prestress on the structure, and at the same time, it also fails to consider the influence of the tower height.

[0010] (3) Some scholars have used the difference iteration method to optimize the cable force during the construction process of a low tower cable-stayed bridge.

[0011] Disadvantages: Manual operation is required for each iteration, the number of iterations is limited, the efficiency is low, and it is not suitable for solving high-dimensional problems; it also does not consider the collaborative optimization with the prestressed steel bars of the main girder.

[0012] (4) Some scholars comprehensively considered the ratio problem of external cables and internal prestressed tendons, taking the structural section stress and the maximum displacement as the constraint conditions, and the minimum cost as the objective function, and sought a set of optimal cable forces and prestresses through the method of value adjustment calculation.

[0013] Disadvantages: The tower height of this optimization method is a fixed value, and the tower height of a low tower cable-stayed bridge determines the eccentricity of the external cable. The optimization of the tower height has a certain impact on the overall optimization, and this method fails to consider it.

[0014] For the problems described above, therefore, an optimization method for the external stay cables, internal prestressed steel bars and bridge towers of a low tower cable-stayed bridge is needed to solve. Summary of the Invention

[0015] The content of the present invention is to provide an optimization method for the external stay cables, internal prestressed steel bars and bridge towers of a low tower cable-stayed bridge, which can overcome certain or some defects of the prior art.

[0016] According to the optimization method for the external stay cables, internal prestressed steel bars and bridge towers of a low tower cable-stayed bridge of the present invention, it includes the following steps:

[0017] Step S1: Regard the cable force, prestress and tower height as variables to be optimized at the same time, deduce the formula for their collaborative optimization, and solve the optimization problem with the help of programming language;

[0018] Step S2: Calculate the influence of the unit cable force of a single stay cable on the stresses of the upper and lower edges of the main girder, and obtain the influence matrix of the cable force after linear superposition. Similarly, obtain the influence matrix of the prestressed steel bars of the top and bottom plates of the main girder;

[0019] Step S3: Take the concrete stress of the main girder meeting the specification requirements as the constraint condition of the optimization problem, and use the penalty function method to incorporate the constraint condition into the optimization objective function;

[0020] Step S4: Establish the functional relationship between the variables to be optimized and the cost, and obtain the values of the optimized variables corresponding to the minimum cost of the tower, cable and steel bars through the optimization algorithm;

[0021] Step S5: Solve the optimization problem multiple times, and statistically obtain the uniform optimization result of the multi-valued function according to the law of large numbers.

[0022] Preferably, in step S2, the genetic algorithm is used to adjust the adjustable vector cable force {T}, the top plate steel bar {P T}, the bottom plate steel bar {P B} and the tower height {H}, and calculate the stresses σ t 、σb .

[0023] Preferably, in step S2, if there are i cables in the low tower cable-stayed bridge, the adjustment vector {T} of the cable forces = {T1, T2,......, T i} T ;

[0024] The low tower cable-stayed bridge is divided into l beam segments according to the construction stage. In the state of a bare beam without cables and tendons, the first j beam segments have negative bending moments, and the adjustment vector {P T} = {N T1 , N T2 ,......, N Tj} T ;

[0025] In the state of a bare beam without cables and tendons, the last k beam segments have positive bending moments, and the adjustment vector {P B} = {N B1 , N B2 ,......, N Bk} T ;

[0026] The tower height {H} is a scalar, representing the distance from the main beam to the outermost cable at the top;

[0027] The bending moment {M D} and axial force {N D} of the bare beam without cables and tendons in the state of the completed bridge under the action of loads are obtained through the Midas Civil model;

[0028] The bending moment of the l beam segment cross-sections under the action of a unit vertical force of the i-th cable Then, when the unit vertical forces of the i cables act together on the l beam segment cross-sections, an influence matrix with l rows and i columns will be obtained.

[0029] Similarly, when the unit longitudinal forces of the i cables act together on the l beam segment cross-sections, an influence matrix with l rows and i columns will also be obtained.

[0030] Similarly, the influence matrix of the unit vertical force and unit longitudinal force of the i cables on the axial force of the l beam segments is

[0031] The influence matrix of the bending moment and axial force generated by the j unit top plate tendons on the l beam segments

[0032] The influence matrix of the bending moment and axial force generated by the k unit bottom plate tendons on the l beam segments

[0033] The upper edge stress is calculated as:

[0034]

[0035] The lower edge stress is calculated as:

[0036]

[0037] σ t 、σ b represent the stresses of the upper and lower edges, negative for compression and positive for tension;

[0038] In the formula, M D and N D represent the bending moment and axial force of l beam segments in the state of no cables and no reinforcement in the first completion of the bridge. The cross-section parameter vectors A, I, C t 、C b are all column vectors of l elements, representing the area, moment of inertia and the distance from the upper and lower edges to the neutral axis of l beam segments respectively; {α} is a column vector of i elements.

[0039] Preferably, {α} represents the angle between each cable and the main girder, and the expression of {α} is:

[0040]

[0041] Among them, L i is the longitudinal distance of the i-th cable from the bridge tower, and H i is the vertical distance of the i-th cable from the main girder on the bridge tower.

[0042] Preferably, in the step S3, according to the specification requirements, the main girder stress should satisfy full-section compression and not exceed the concrete compressive design strength, that is, the optimized control conditions are shown in formulas (3) and (4);

[0043] σ a ≤σ t ≤0 (3)

[0044] σ a ≤σ b ≤0 (4)

[0045] Among them, σ a is the design value of the concrete compressive strength and is negative.

[0046] Preferably, in the step S3, formulas (3) and (4) are used for σ t 、σ bJudge whether it meets the specification requirements. If the requirements of formulas (3) and (4) are not met, output a maximum value as the total cost of the external cable, internal prestressed tendons and bridge tower. If the requirements of formulas (3) and (4) are met, proceed to the next step to calculate the total cost of the external cable, internal prestress and bridge tower.

[0047] Preferably, in step S3, using the principle of formula (5), a more adaptable calculation formula (6) is obtained by deformation, and the total cost of the external cable, internal prestress and bridge tower is calculated using formula (6); formulas (5) and (6) are as follows:

[0048] W = χ1W C +W S +χ2W T (5)

[0049]

[0050] W C 、W S 、W T represent the weights of the stay cables, prestressed tendons and bridge tower. Considering that the material unit prices, construction costs and later maintenance costs of the stay cables, prestressed tendons and bridge tower vary greatly, the same-weight unit price ratio χ1 of the stay cables and prestressed tendons and the same-weight unit price ratio χ2 of the bridge tower and prestressed tendons are introduced, and the total cost of the cables and tendons is expressed by formula (5);

[0051] In formula (6), ρ C 、ρ S 、ρ T represent the unit weights of the stay cables, prestressed tendons and bridge tower respectively, T i is the cable force of the stay cable, f k is the design value of the tensile strength of the stay cable, γ C is the safety factor of the stay cable, i represents the number of stay cables, L Ci is the length of the stay cable; A Sj 、A Sk are the areas of the unit prestressed tendons of the top and bottom slabs, P j 、P k are the numbers of prestressed tendons of the top and bottom slabs, i and j represent the beam segments that need to be reinforced, L Sj 、L Sk are the lengths of the prestressed tendons of the top and bottom slabs; A T is the cross-sectional area of the bridge tower, and H is the tower height.

[0052] Preferably, in step 4, the optimization calculation method:

[0053] The first-step optimization: Each time the adjustment vector is adjusted, a total cost will be obtained. If equations (3) and (4) are not satisfied, an abnormally large value will be obtained. If equations (3) and (4) are satisfied, a normal total cost value will be obtained. The program will compare these cost values to obtain the adjustment vector corresponding to the minimum cost.

[0054] The second-step optimization: Through the previous step, a set of adjustment vectors corresponding to the minimum total cost can be obtained. By performing the previous step multiple times, multiple sets of adjustment vector solutions corresponding to the minimum cost can be obtained, and statistical analysis can be carried out according to the law of large numbers to obtain a more uniform optimization result to adapt to the actual engineering design.

[0055] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0056] The present invention comprehensively considers the problems of the tower, beam, and cables of the low tower cable-stayed bridge, transforms them into a high-dimensional optimization problem with simple theory, and uses a computer to solve the high-dimensional optimization problem.

[0057] The present invention can comprehensively optimize the design of the low tower cable-stayed bridge. It is applicable to the condition where the main beam section design and the number and position of stay cables have been determined. By adjusting the parameters of external cables, internal prestressed tendons, and tower height, the load can be reasonably distributed, and the minimum cost of the cable, tendon, and tower can be sought. Brief Description of the Drawings

[0058] Figure 1 It is a flowchart of an optimization method for external stay cables, internal prestressed tendons, and bridge towers of a low tower cable-stayed bridge in Embodiment 1;

[0059] Figure 2 It is an elevation view of the whole bridge of the low tower cable-stayed bridge in Embodiment 2;

[0060] Figure 3(a) is a Midas whole-bridge main beam model of the low tower cable-stayed bridge in Embodiment 2;

[0061] Figure 3(b) is a Midas mid-span main beam model of the low tower cable-stayed bridge in Embodiment 2;

[0062] Figure 4(a) is a bending moment diagram of the left half-span of the low tower cable-stayed bridge without cables and tendons in Embodiment 2;

[0063] Figure 4(b) is an axial force diagram of the left half-span of the low tower cable-stayed bridge without cables and tendons in Embodiment 2;

[0064] Figure 5(a) is a bending moment diagram of the left half-span of the low tower cable-stayed bridge under the action of a vertical unit force of stay cable No. 1 (S1) in Embodiment 2;

[0065] Figure 5(b) is an axial force diagram of the left half-span of the low tower cable-stayed bridge under the action of a vertical unit force of stay cable No. 1 (S1) in Embodiment 2;

[0066] Figure 5(c) shows the bending moment diagram of the left half-span of the low tower cable-stayed bridge under the action of a vertical unit force on the 18th stay cable (S18) in Example 2;

[0067] Figure 5(d) shows the axial force diagram of the left half-span of the low tower cable-stayed bridge under the action of a vertical unit force on the 18th stay cable (S18) in Example 2;

[0068] Figure 6(a) shows the bending moment diagram of the left half-span of the low tower cable-stayed bridge under the action of a horizontal unit force on the 1st stay cable (S1) in Example 2;

[0069] Figure 6(b) shows the axial force diagram of the left half-span of the low tower cable-stayed bridge under the action of a horizontal unit force on the 1st stay cable (S1) in Example 2;

[0070] Figure 6(c) shows the bending moment diagram of the left half-span of the low tower cable-stayed bridge under the action of a horizontal unit force on the 18th stay cable (S18) in Example 2;

[0071] Figure 6(d) shows the axial force diagram of the left half-span of the low tower cable-stayed bridge under the action of a horizontal unit force on the 18th stay cable (S18) in Example 2;

[0072] Figure 7(a) shows the bending moment diagram of the left half-span of the low tower cable-stayed bridge under the action of the unit top plate bundle T1 in Example 2;

[0073] Figure 7(b) shows the axial force diagram of the left half-span of the low tower cable-stayed bridge under the action of the unit top plate bundle T1 in Example 2;

[0074] Figure 7(c) shows the bending moment diagram of the left half-span of the low tower cable-stayed bridge under the action of the unit top plate bundle T12 in Example 2;

[0075] Figure 7(d) shows the axial force diagram of the left half-span of the low tower cable-stayed bridge under the action of the unit top plate bundle T12 in Example 2;

[0076] Figure 8(a) shows the bending moment diagram of the left half-span of the low tower cable-stayed bridge under the action of the unit bottom plate bundle B1 in Example 2;

[0077] Figure 8(b) shows the axial force diagram of the left half-span of the low tower cable-stayed bridge under the action of the unit bottom plate bundle B1 in Example 2;

[0078] Figure 8(c) shows the bending moment diagram of the left half-span of the low tower cable-stayed bridge under the action of the unit bottom plate bundle B10 in Example 2;

[0079] Figure 8(d) shows the axial force diagram of the left half-span of the low tower cable-stayed bridge under the action of the unit bottom plate bundle B10 in Example 2;

[0080] Figure 9 It is the comparison diagram of the low tower cable-stayed bridge in Example 2 before and after the first cable force optimization;

[0081] Figure 10 It is the comparison diagram of the low tower cable-stayed bridge in Example 2 before and after the second cable force optimization;

[0082] Figure 11 It is the comparison diagram of the upper and lower edge stresses before and after the second optimization of the low tower cable-stayed bridge in Embodiment 2;

[0083] Figure 12(a) is the comparison diagram of the top plate reinforcement usage before and after the optimization in Embodiment 2;

[0084] Figure 12(b) is the comparison diagram of the bottom plate reinforcement usage before and after the optimization in Embodiment 2. Specific implementation manners

[0085] To further understand the content of the present invention, the present invention will be described in detail in combination with the accompanying drawings and embodiments. It should be understood that the embodiments are only for explaining the present invention rather than limiting it.

[0086] Embodiment 1

[0087] As Figure 1 shown, this embodiment provides an optimization method for the external stay cables, internal prestressed tendons and bridge towers of a low tower cable-stayed bridge, which includes the following steps:

[0088] Step S1: Simultaneously regard the cable force, prestress and tower height as variables to be optimized, deduce the formula for their collaborative optimization, and solve the optimization problem with the help of programming languages;

[0089] Step S2: Calculate the influence of the unit cable force of a single stay cable on the upper and lower edge stresses of the main girder, and obtain the influence matrix of the cable force after linear superposition. Similarly, obtain the influence matrix of the prestressed steel bars of the top and bottom plates of the main girder;

[0090] Use the genetic algorithm to adjust the adjusted vector of the cable force {T}, the top plate reinforcement {P T}, the bottom plate reinforcement {P B} and the tower height {H}, and calculate the upper and lower edge stresses σ t , σ b of the main girder by using the adjusted adjusted vector.

[0091] In the said step S2, if there are i stay cables in the low tower cable-stayed bridge, the adjusted vector {T} composed of the cable forces = {T1, T2,......, T i} T ;

[0092] Divide the low tower cable-stayed bridge into l beam segments according to the construction stage. In the state of a bare beam without stay cables and reinforcements, the first j beam segments are negative bending moments, then the adjusted vector {P T} = {N T1 , N T2 ,......, N Tj} T ;

[0093] In the state of a bare beam without stay cables and reinforcements, the last k beam segments are positive bending moments, then the adjusted vector {PB} = {N B1 , N B2 ,......, N Bk} T ;

[0094] The tower height {H} is a scalar, representing the distance from the main girder to the outermost external cable at the top. In this example, the principle of tower height adjustment is not to change the distance of the cable area on the tower and the vertical cable spacing. The cable area moves up and down with the change of the tower height;

[0095] The bending moment {M D} and axial force {N D} of the bare beam state without cables and reinforcements under load at the time of initial bridge completion are obtained through the Midas Civil model;

[0096] The bending moment of the l beam segments at the cross-section under the action of a unit vertical force (100 KN) of the No. 1 cable The bending moment of the l beam segments at the cross-section under the action of a unit vertical force of the i-th cable Then, when the bending moments of the l beam segments at the cross-section are under the combined action of the unit vertical forces of the i cables, an influence matrix of l rows and i columns will be obtained,

[0097] Similarly, when the bending moments of the l beam segments at the cross-section are under the combined action of the unit longitudinal forces of the i cables, an influence matrix of l rows and i columns will also be obtained,

[0098] Similarly, the influence matrix of the unit vertical forces and unit longitudinal forces of the i cables on the axial forces of the l beam segments is

[0099] The influence matrix of the bending moment and axial force generated by the j unit top plate bundles on the l beam segments

[0100] The influence matrix of the bending moment and axial force generated by the k unit bottom plate bundles on the l beam segments

[0101] The calculation of the upper edge stress is:

[0102]

[0103] The calculation of the lower edge stress is:

[0104]

[0105] σ t 、σ b represent the stresses of the upper and lower edges, negative for compression and positive for tension;

[0106] In the formula, MD With N D It represents the bending moment and axial force of l beam segments in the state of a single-span bridge without cables and tendons. The cross-section parameter vectors A, I, and C t , C b are all column vectors with l elements, representing the area, moment of inertia, and the distance from the upper and lower edges to the neutral axis of l beam segments respectively. These parameters can all be exported by Midas Civil.

[0107] Step S3: Taking the concrete stress of the main girder meeting the specification requirements as the constraint condition of the optimization problem, the penalty function method is used to incorporate the constraint condition into the optimization objective function;

[0108] {α} is a column vector with i elements, representing the angle between each cable and the main girder. The expression of {α} is:

[0109]

[0110] where L i is the longitudinal distance of the i-th cable from the bridge tower, and H i is the vertical distance of the i-th cable from the main girder on the bridge tower.

[0111] According to the specification requirements, the stress of the main girder should satisfy that the whole cross-section is in compression and does not exceed the concrete compressive design strength, that is, the optimization control conditions are shown in formulas (3) and (4);

[0112] σ a ≤σ t ≤0 (3)

[0113] σ a ≤σ b ≤0 (4)

[0114] where σ a is the design value of the concrete compressive strength and is negative.

[0115] Using formulas (3) and (4) to judge whether σ t , σ b meets the specification requirements. If it does not meet the requirements of formulas (3) and (4), an extremely large value is output as the total cost of the external cables, internal prestressing tendons, and bridge towers; if it meets the requirements of formulas (3) and (4), the next step is to calculate the total cost of the external cables, internal prestressing, and bridge towers.

[0116] In the said step S3, using the principle of formula (5), a more adaptable calculation formula (6) is obtained through deformation, and the total cost of the external cables, internal prestressing, and bridge towers is calculated using formula (6); Formulas (5) and (6) are as follows:

[0117] W = χ1W C +W S +χ2WT (5)

[0118]

[0119] W C , W S , W T represents the weight of the cable, prestressed tendons and bridge towers. Considering that the material unit price, construction cost and later maintenance cost of the cable, prestressed tendons and bridge towers are quite different, the unit price ratio of the same weight of the cable and prestressed tendons χ1 and the unit price ratio of the same weight of the bridge tower and prestressed tendons χ2 are introduced. The total cost of the cable and tendons is expressed by formula (5);

[0120] In formula (6), ρ C , S , T Respectively represent the bulk density of the cable, prestressed tendons and bridge towers, T i is the cable force of the inclined cable, f k is the design value of the tensile strength of the cable, γ C is the safety factor of the cable, i represents the number of cables, L Ci is the length of the inclined cable; A Sj , A Sk is the area of ​​unit prestressed tendons in the top and bottom slabs, P j , P k The number of prestressed bars in the top and bottom slabs, i and j represent the number of beam sections that need reinforcement, and L Sj , L Sk A is the length of the prestressed tendons of the top and bottom plates; T is the cross-sectional area of ​​the bridge tower, and H is the tower height.

[0121] Step S4, establishing a functional relationship between the variables to be optimized and the cost, and obtaining the optimized variable value corresponding to the minimum cost of the tower cable reinforcement through the optimization algorithm;

[0122] In step 4, the calculation method is optimized:

[0123] The first step of optimization: Each time the adjustment vector is adjusted, a total cost will be obtained. If it does not satisfy equations (3) and (4), an abnormally large value will be obtained. If it satisfies equations (3) and (4), a normal total cost value will be obtained. The program will compare these cost values ​​and obtain the adjustment vector corresponding to the minimum cost.

[0124] The second step of optimization: Through the previous step, a set of adjustment vectors with the minimum total cost can be obtained. The previous step can be repeated multiple times to obtain multiple sets of adjustment vector solutions with the minimum cost. According to the law of large numbers, statistics can be used to obtain a more uniform optimization result to adapt to the actual engineering design.

[0125] Step S5: Solve the optimization problem multiple times. According to the law of large numbers, the uniform optimization result of the multi-valued function is obtained.

[0126] In this embodiment, the problems of the tower, beam, and cables of the low tower cable-stayed bridge are comprehensively considered, transformed into a high-dimensional optimization problem with a simple theory, and a computer is used to solve the high-dimensional optimization problem. This embodiment is applicable to the condition that the main beam section design, the number and position of the stay cables have been determined. By adjusting the parameters of the external cable, the internal prestressed tendons, and the tower height, the load is reasonably distributed, and the minimum cost of the cable, tendon, and tower is sought.

[0127] Embodiment 2:

[0128] Taking a certain actual engineering bridge example to verify the feasibility of this method.

[0129] As Figure 2 shown, the original bridge is a three-tower four-span symmetric structure. The stay cables are double cable planes, arranged in a fan shape, with 18 pairs on each side, and a total of 216 cables on 6 sides of the whole bridge. Each stay cable consists of 73 Φ j 15.24 epoxy-coated steel strands, and the strength of the steel strands

[0130] The original bridge adopts symmetric cantilever construction. The middle span is divided into 28 beam segments (block 0 to block 27) on both the left and right sides, and the middle 28th block is the closure block. The whole bridge is a symmetric structure. To simplify the calculation, the left half of the middle span is taken as the calculation object. The Midas full-bridge main beam model and the middle span calculation model are shown in Figure 3. Since the tower height is a variable in this method, only the main beam model needs to be built during modeling.

[0131] As shown in Figure 4, use Midas to calculate the bending moment and internal forces M D , N D .

[0132] Due to the structural symmetry, only half of the structure can be selected to study the design variables and state variables. In this structure, 18 cables, 12 types of top plate tendons, 10 types of bottom plate tendons, and the tower height are selected as variables, a total of 41. The stresses at the upper and lower edges of 29 sections are used as state variables, a total of 58. There is one objective function, that is, the total cost of the cable, tendon, and tower.

[0133] The bending moment and axial force generated by the unit vertical force of a single cable on 29 beam segments are shown in Figure 5. By exporting the data, the influence matrix of the vertical components of the 18 cable forces on the bending moment and axial force generated by 29 beam segments can be obtained as

[0134] Similarly, the bending moment and axial force generated by the unit horizontal force of a single cable on 29 beam segments are shown in Figure 6. By exporting the data, the influence matrix of the horizontal components of the 18 cable forces on the bending moment and axial force generated by 29 beam segments can be obtained as

[0135] In the bare beam state, the negative moment zone beam section is selected to arrange the top plate prestressing tendons. In this example, 12 types of top plate beams are arranged. The moment axial force generated by the unit top plate beam is shown in Figure 7. The influence matrix of the moment axial force generated by the 12 unit top plate beams on the 29 beam sections is:

[0136] In the bare beam state, the beam section in the positive moment zone is selected to arrange the bottom plate prestressing tendons. In this example, 10 types of bottom plate tendons are arranged. The moment axial force generated by the unit bottom plate tendon is shown in Figure 8. The influence matrix of the moment axial force generated by 10 unit bottom plate tendons on 29 beam sections is:

[0137] Write a program to use the genetic algorithm optimization program to find the minimum value of the objective function. Import the previously obtained data into the program and use equations (1) and (2) to calculate the stress of the upper and lower edges, and use equations (3) and (4) to determine whether it meets the requirements of the specification, that is, the entire section is compressed and does not exceed the design compressive strength of the material. If the calculated upper and lower edge stresses do not meet equations (3) and (4), a very large value is output, and the population is "eliminated"; if the calculated upper and lower edge stresses meet equations (3) and (4), the objective function value is calculated and the minimum objective function value is iterated for the next time until the corresponding number of iterations is met.

[0138] Debug the corresponding parameters of the program, select the appropriate population number and number of iterations in the algorithm, and seek the minimum value of the objective function, that is, the minimum cost W min .

[0139] like Figure 9 As shown in the figure, this method uses genetic algorithm to obtain 50 sets of optimized cable forces and makes a preliminary comparison with the cable forces before optimization (three sets are listed in this figure). Considering that in actual projects, in order to facilitate construction, too many types of inclined cables and prestressed tendons should be avoided as much as possible, the 50 sets of data need to be processed again, that is, the second step of cable force optimization.

[0140] The standard deviation method was used to process 50 groups of data. After removing the outliers, the average values ​​of 41 variables were obtained. The cable forces of 1# to 4# cables were taken as 8000KN, the cable forces of 5# to 15# cables were taken as 22000KN, and the cable forces of 16#, 17#, and 18# cables were taken as 16000KN. The cable forces were compared with those before optimization. Figure 10 shown.

[0141] The cable forces and prestressed tendons after the optimization in the second step are tested, and the upper and lower edge stresses before and after the optimization are compared. Figure 11 The comparison of the amount of prestressed tendons before and after optimization is shown in Figure 12.

[0142] After the inspection meets the specification requirements, use formula (6) to calculate the total cost of the optimized cable-strut tower and compare it with the cost of the cable-strut tower before optimization. The results show that the cost of the cable before optimization is 710 unit costs, and the cost of the cable after optimization is 533 unit costs; the cost of the prestressed tendon before optimization is 165 unit costs, and the cost of the prestressed tendon after optimization is 42.8 unit costs; the cost of the tower before optimization is 139 unit costs, and the cost of the tower after optimization is 147 unit costs; the total cost before optimization is 1014 unit costs, and the total cost after optimization is 722.8 unit costs. The total cost of the cable-strut tower calculated by this method is 71.3% of the original design, which has certain practicality.

[0143] The above has schematically described the present invention and its implementation manners. This description is not restrictive. What is shown in the drawings is only one of the implementation manners of the present invention, and the actual structure is not limited thereto. Therefore, if those of ordinary skill in the art are inspired by it and, without departing from the gist of the present invention, design similar structural manners and embodiments to this technical solution without creative efforts, they shall fall within the protection scope of the present invention.

Claims

1. An optimization method for external stay cables, internal prestressed tendons and bridge towers of a low-tower cable-stayed bridge, characterized by: The following steps are involved: Step S1, treating the cable force, prestress and tower height as variables to be optimized, deriving their collaborative optimization formula, and solving the optimization problem with the help of a programming language; Step S2, calculating the influence of the unit cable force of a single cable on the stress of the upper and lower edges of the main beam, and obtaining the influence matrix of the cable force after linear superposition, and similarly obtaining the influence matrix of the prestressed steel bars of the top and bottom plates of the main beam; In step S2, a genetic algorithm is used to adjust the applied vector cable force {T}, the top plate reinforcement {P T }、Bottom ribs {P B } and tower height {H}, and use the adjusted adjustment vector to calculate the stress σ at the upper and lower edges of the main beam t , σ b ; Step S3, taking the main beam concrete stress meeting the specification requirements as the constraint condition of the optimization problem, and incorporating the constraint condition into the optimization objective function using the penalty function method; In step S3, according to the specification requirements, the main beam force should satisfy the full cross-section compression and cannot exceed the concrete compressive design strength, that is, the optimized control conditions are shown in equations (3) and (4); s a ≤σ t ≤0 (3) s a ≤σ b ≤0 (4) where σ a is the design value of concrete compressive strength, which is a negative value; In step S3, the principle of formula (5) is used to transform a more suitable calculation formula (6), and the total cost of the external cables, internal prestressing and bridge towers is calculated using formula (6); formula (5) and formula (6) are as follows: W=χ1W C +W S +χ2W T (5) W C , W S , W T represents the weight of the cable, prestressed tendons and bridge towers. Considering the large differences in the unit price of materials, construction costs and later maintenance costs of the cable, prestressed tendons and bridge towers, the unit price ratio of the same weight of the cable and prestressed tendons χ1 and the unit price ratio of the same weight of the bridge tower and prestressed tendons χ2 are introduced. The total cost of the cable and tendons is expressed by formula (5); In formula (6), ρ C , S , T Respectively represent the bulk density of the cable, prestressed tendons and bridge towers, T i is the cable force of the inclined cable, f k is the design value of the tensile strength of the cable, γ C is the safety factor of the cable, i represents the number of cables, L Ci is the length of the inclined cable; A Sj , A Sk is the area of ​​unit prestressed tendons in the top and bottom slabs, P j , P k The number of prestressed bars in the top and bottom slabs, i and j represent the number of beam sections that need reinforcement, and L Sj , L Sk A is the length of the prestressed tendons of the top and bottom plates; T is the cross-sectional area of ​​the bridge tower, and H is the tower height; Step S4, establishing a functional relationship between the variables to be optimized and the cost, and obtaining the optimized variable value corresponding to the minimum cost of the tower cable reinforcement through the optimization algorithm; In step S4, the calculation method is optimized: The first step of optimization: Each time the adjustment vector is adjusted, a total cost will be obtained. If it does not satisfy equations (3) and (4), an abnormally large value will be obtained. If it satisfies equations (3) and (4), a normal total cost value will be obtained. The program will compare these cost values ​​and obtain the adjustment vector corresponding to the minimum cost. The second step is optimization: through the previous step, a set of adjustment vectors with the minimum total cost can be obtained. The previous step can be repeated many times to obtain multiple sets of adjustment vector solutions with the minimum cost. According to the law of large numbers, statistics can be obtained to obtain a more uniform optimization result to adapt to the actual engineering design. Step S5: solve the optimization problem multiple times and obtain a uniform optimization result of the multi-valued function according to the law of large numbers.

2. The optimization method for external stay cables, internal prestressed tendons and bridge towers of a low-tower cable-stayed bridge according to claim 1 is characterized by: In step S2, the short-tower cable-stayed bridge has a total of i cables, and the adjustment vector {T} composed of the cable forces is {T1, T2, ..., T i } T ; The low-tower cable-stayed bridge is divided into l beam segments according to the construction stage. In the state of bare beam without cables and reinforcement, the first j beam segments are negative bending moments. Then the adjustment vector {P T }={N T1 ,N T2 ,......,N Tj } T ; In the state of bare beam without cable and reinforcement, the last k beam segments are positive bending moments, then the adjustment vector {P B }={N B1 ,N B2 ,......,N Bk } T ; The tower height {H} is a scalar quantity, indicating the distance from the main beam to the topmost external cable; The bending moment {M D } and axial force {N D }; The bending moment of the lth beam section under the unit vertical force of cable i Then, when the bending moments of the l beam sections act together with the unit vertical forces of the i cables, an influence matrix with l rows and i columns will be obtained. Similarly, when the bending moments of l beam sections act together with the unit horizontal forces of i cables, an influence matrix with l rows and i columns will be obtained. Similarly, the influence matrix of the unit vertical force and unit horizontal force of i cables on the axial force of l beam sections is: The influence matrix of the bending moment and axial force generated by j unit top plate beams on l beam segments The influence matrix of the bending moment and axial force generated by k unit bottom plate beams on l beam segments The upper edge stress is calculated as: The stress at the lower edge is calculated as: σ t , σ b It represents the stress at the upper and lower edges, with compression being negative and tension being positive; Where M D With N D It represents the bending moment and axial force of a beam segment in a completed bridge without cables or reinforcement. The section parameter vectors A, I, and C t , C b are all column vectors with l elements, representing the area, moment of inertia and distance from the upper and lower edges to the neutral axis of the l beam segments respectively; {α} is a column vector with i elements; {α} represents the angle between each cable and the main beam. The expression of {α} is: Among them, L i is the longitudinal distance between cable No. i and the bridge tower, H i is the vertical distance between cable No. i and the main beam on the bridge tower.

3. The optimization method for external stay cables, internal prestressed tendons and bridge towers of a low-tower cable-stayed bridge according to claim 2 is characterized by: In step S3, equations (3) and (4) are used to calculate σ t , σ b It is judged whether it meets the requirements of the specification. If it does not meet the requirements of formula (3) and (4), a maximum value is output as the total cost of the external cables, internal prestressed tendons and bridge towers; if it meets the requirements of formula (3) and (4), it proceeds to the next step to calculate the total cost of the external cables, internal prestressed tendons and bridge towers.

Images