Longitudinal elastic cable constraint system design method and cable-stayed bridge design method

Abstract

The application relates to a longitudinal elastic cable constraint system design method and a cable-stayed bridge design method, which comprises the following steps: fixing the longitudinal constraint of a middle tower, calculating a plurality of elastic cable cross-sectional areas according to the longitudinal constraint force under a plurality of stress working conditions and an elastic cable structure safety coefficient, and taking the maximum value of the plurality of elastic cable cross-sectional areas as an elastic cable cross-sectional area design value; and determining the cable length according to the elastic cable cross-sectional area design value and the maximum longitudinal displacement amount of a main beam. According to the application, the elastic cable cross-sectional area is determined first, and then the cable length is determined according to the elastic cable cross-sectional area design value and the maximum longitudinal displacement amount of the main beam. Since the elastic cable cross-sectional area has been determined, only the elastic cable length needs to be tried, and compared with the case that the elastic cable cross-sectional area and the elastic cable length are both uncertain, the trial workload can be greatly reduced, so that the longitudinal elastic cable key parameters can be quickly and effectively determined, and favorable conditions are created for subsequent deepening design of the bridge scheme.

Description

Technical Field

[0001] This application relates to the technical field of bridge engineering, and in particular to a design method for a longitudinal elastic cable restraint system and a design method for cable-stayed bridges. Background Technology

[0002] Currently, with economic and social development, people's demand for transportation is increasing, and there are more and more bridges over major rivers. The number of available bridge sites for new bridges is decreasing. Due to the influence of navigation, flood control and existing building pipelines, the requirements for bridge spans are also increasing.

[0003] Due to the scarcity of river-crossing passage resources, the construction of new bridges is currently recommended to adopt a combined road and rail approach. Currently completed and operational kilometer-long road-rail cable-stayed bridges are typically two-tower cable-stayed bridges; no examples of kilometer-long road-rail three-tower cable-stayed bridges have been found to date.

[0004] When the span of a dual-purpose (road and rail) cable-stayed bridge reaches the kilometer level, the main differences between a three-tower and a two-tower bridge are: ① the main girder has a longer span and larger end expansion and contraction displacements; ② due to the lack of anchor cables and anchor piers in the middle tower, the main bridge has lower stiffness; ③ the zero temperature point is located at the middle tower, rather than at the mid-span of the main span. Based on these characteristics, a longitudinal elastic cable restraint system is more suitable for a kilometer-level dual-purpose (road and rail) three-tower cable-stayed bridge. The key parameters of the longitudinal elastic cable are the cross-sectional area As and the cable length Ls.

[0005] In related technologies, the current method for determining the cross-sectional area and length of an elastic cable is as follows: First, establish a finite element model, set a longitudinal spring in the central tower and assign it an initial stiffness, and calculate the beam end displacement; Second, set a limit value for the beam end displacement, and continuously modify the spring stiffness until the limit value is met, at which point the spring stiffness is determined; Third, use the elastic cable stiffness formula K = E s ·A s / L s E s Let L be the elastic modulus of the elastic cable, and let L be the initial cable length. s0 The corresponding cable area is As0. For each set of data (L... s0 A s0 Substituting the values ​​into the model for trial calculations, the elastic cable force was obtained. Then, it was checked whether the stress met the specification requirements. After repeated trial calculations, a reasonable value (L) was finally determined. s A s ).

[0006] However, the methods in the relevant technologies involve multiple trial calculations. Due to the complexity of the finite element model and the large number of element nodes, repeated trial calculations consume a lot of time and effort. Summary of the Invention

[0007] This application provides a design method for a longitudinal elastic cable constraint system and a cable-stayed bridge design method to solve the problem in related technologies that the methods for determining the cross-sectional area and length of the elastic cable involve multiple trial calculations, and that repeated trial calculations consume a lot of time and effort due to the complexity of the finite element model and the large number of element nodes.

[0008] On the one hand, this application provides a design method for a longitudinally elastic cable restraint system, and the technical solution adopted is:

[0009] A design method for a longitudinally elastic cable-constrained system, comprising:

[0010] The longitudinal constraint of the central tower is set to be fixed. Based on the longitudinal constraint force and the safety factor of the elastic cable structure under multiple stress conditions, multiple elastic cable cross-sectional areas are calculated. The maximum value of multiple elastic cable cross-sectional areas is taken as the design value of the elastic cable cross-sectional area.

[0011] The cable length is determined based on the design value of the cross-sectional area of ​​the elastic cable and the maximum longitudinal displacement of the main beam.

[0012] In some embodiments, the calculation of multiple elastic cable cross-sectional areas based on the longitudinal constraint force and the safety factor of the elastic cable structure under multiple stress conditions includes:

[0013] According to formula A s =T / (μ×[σ s ]), calculate the cross-sectional area of ​​the elastic cable;

[0014] Among them, A s For the cross-sectional area of ​​the elastic cable, σ s Let T be the allowable stress value of the elastic cable, T be the longitudinal constraint force, and μ be the safety factor of the elastic cable structure.

[0015] In some embodiments, determining the cable length based on the design value of the elastic cable cross-sectional area and the maximum longitudinal displacement of the main beam includes:

[0016] Substitute the design value of the cross-sectional area of ​​the elastic cable and the initial cable length into the finite element model, calculate the longitudinal displacement of the main beam under the cable length, and determine whether the longitudinal displacement of the main beam is less than or equal to the maximum longitudinal displacement of the main beam. If not, adjust the cable length value until the corresponding longitudinal displacement of the main beam is less than or equal to the maximum longitudinal displacement of the main beam, and the difference is minimized.

[0017] In some embodiments, the cable length is an integer multiple of the length of the main beam section.

[0018] In some embodiments, after determining the cable length, the pretension of the elastic cable is determined based on the comprehensive reduction factor of the live load under normal operating conditions and the longitudinal constraint force generated by the live load under normal operating conditions when fixed with longitudinal constraints.

[0019] In some embodiments, determining the pretension of the elastic cable based on the comprehensive reduction factor of the live load under normal operating conditions and the longitudinal constraint force generated by the live load under normal operating conditions when fixed with longitudinal constraints includes:

[0020] According to formula F s =λT 活 Determine the pretension of the elastic cable;

[0021] Among them, F s T represents the pretension of the elastic cable, λ represents the comprehensive reduction factor for live load under normal operating conditions, and T represents the pretension of the elastic cable. 活 The longitudinal constraint force is the longitudinal constraint force generated by the live load under normal operating conditions when the longitudinal constraint is fixed.

[0022] On the other hand, this application provides a cable-stayed bridge design method, characterized by comprising:

[0023] Determine the span of the middle span, the height of the middle tower, the span of the side spans, and the height of the side towers;

[0024] Determine the parameters of the elastic cable restraint system between the central tower and the main beam;

[0025] Determine the stiffness, bending moment, and column spacing of the central tower;

[0026] Determine the distance between the auxiliary pier and the side pier;

[0027] The parameters for determining the elastic cable restraint system between the central tower and the main beam include:

[0028] The longitudinal constraint of the central tower is set to be fixed. Based on the longitudinal constraint force and the safety factor of the elastic cable structure under multiple stress conditions, multiple elastic cable cross-sectional areas are calculated. The maximum value of multiple elastic cable cross-sectional areas is taken as the design value of the elastic cable cross-sectional area.

[0029] The cable length is determined based on the design value of the cross-sectional area of ​​the elastic cable and the maximum longitudinal displacement of the main beam.

[0030] In some embodiments, determining the stiffness of the central tower, the bending moment of the central tower, and the spacing between the central tower columns includes:

[0031] Determine the stiffness of the middle tower based on the vertical displacement of the main beam;

[0032] Determine the bending moment of the middle tower based on its stiffness.

[0033] In some embodiments, determining the stiffness of the central tower based on the vertical displacement of the main beam includes:

[0034] The stiffness of the middle tower is determined according to the formula S=α1×B;

[0035] The bending moment of the middle tower is determined according to the formula M=α2×B;

[0036] Where S is the vertical displacement of the main beam, B is the stiffness of the middle tower, M is the bending moment of the middle tower, α15 is the proportionality coefficient of the vertical displacement of the main beam with the stiffness of the middle tower, and α2 is the bending moment of the middle tower with the stiffness of the middle tower.

[0037] The proportional coefficient of degree change.

[0038] In some embodiments, the stiffness of the middle tower is determined based on the maximum vertical displacement of the main beam, and the minimum bending moment of the middle tower is determined based on the stiffness of the middle tower.

[0039] The beneficial effects of the technical solution provided in this application include: This application provides a design method for a longitudinal elastic cable constraint system. By setting the longitudinal constraint of the central tower to be fixed, multiple elastic cable cross-sectional areas are calculated based on the longitudinal constraint force and the safety factor of the elastic cable structure under multiple stress conditions. The maximum value of these multiple elastic cable cross-sectional areas is taken as the design value of the elastic cable cross-sectional area. Therefore, the elastic cable cross-sectional area can be determined first.

[0040] Then, when determining the cable length based on the design value of the elastic cable cross-sectional area and the maximum longitudinal displacement of the main beam, since the cross-sectional area of ​​the elastic cable has already been determined, only trial calculations of the elastic cable length are needed. Compared to the previous calculations, this is much easier.

[0041] When the cross-sectional area and length of the elastic cable are uncertain, trial calculations can be performed, which can greatly reduce the workload of trial calculations and thus quickly and effectively determine the key parameters of the longitudinal elastic cable, creating favorable conditions for the subsequent detailed design of the bridge scheme. Attached Figure Description

[0042] 0 To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0043] Figure 1 A schematic diagram of the overall structure of a kilometer-long dual-purpose (road and rail) three-tower cable-stayed bridge provided in this application embodiment;

[0044] Figure 2 A schematic diagram of the side tower structure of a kilometer-long dual-purpose (road and rail) three-tower cable-stayed bridge provided in an embodiment of this application;

[0045] Figure 3 A schematic diagram of the middle tower structure of a kilometer-long dual-purpose (road and rail) three-tower cable-stayed bridge provided in an embodiment of this application;

[0046] Figure 4 A schematic elevation of the longitudinal elastic cable of a kilometer-long dual-purpose (road and rail) three-tower cable-stayed bridge provided in an embodiment of this application;

[0047] Figure 5 A schematic diagram of the longitudinal elastic cable of a kilometer-long road-rail dual-purpose three-tower cable-stayed bridge provided in an embodiment of this application;

[0048] Figure 6 A schematic diagram of the longitudinal elastic cable and main beam anchorage of a kilometer-long dual-purpose (road and rail) three-tower cable-stayed bridge provided in this application embodiment.

[0049] In the diagram: 1. Side tower; 101. Side tower column; 102. Side tower lower crossbeam; 2. Middle tower; 201. Middle tower column; 202. Middle tower lower crossbeam; 203. Lower crossbeam elastic cable pad; 3. Main beam; 4. Stay cable; 5. Side pier; 6. Auxiliary pier; 7. Elastic cable. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0051] When designing a kilometer-long, dual-purpose (road and rail) three-tower cable-stayed bridge, a longitudinal elastic cable scheme was adopted to reduce the bridge's dynamic response. Due to the large longitudinal constraint force under the main and additional forces, high-strength steel wire was used as the elastic cable material. The key parameter of the longitudinal elastic cable is the cross-sectional area A of the elastic cable. s and cable length L s .

[0052] Currently, the traditional method for determining the cross-sectional area A of an elastic cable is... s and cable length L s The method is as follows: First, determine the longitudinal displacement limit of the main beam, and then calculate the stiffness K of the elastic cable. The stiffness K = E s ·A s / L s E s Given the elastic modulus of the elastic cable, K is determined, and A... s / L s As a constant, an initial cable length L is given. s0 According to the corresponding data (L) s0 A s0 Substituting the values ​​into the model and performing repeated calculations, we obtained the stress (L) that meets the specification requirements. s A s This method involves multiple trial calculations, and due to the complexity of the finite element model and the large number of element nodes, repeated trial calculations consume a lot of time and effort.

[0053] Reference Figure 1-6 The diagram shown is a structural schematic of a kilometer-long dual-purpose road-rail three-tower cable-stayed bridge provided in this application, including a main girder 3, a central tower 2, two side towers 1, two side piers 5, two auxiliary piers 6, and cable stays 4. The connection between the central tower 2 and the main girder 3 adopts a longitudinal elastic cable 7 scheme.

[0054] Specifically, the side tower 1 includes a side tower column 101 and a side tower lower crossbeam 102, the middle tower 2 includes a middle tower column 201 and a middle tower lower crossbeam 202, and the longitudinal elastic cable 7 restraint system includes multiple longitudinal elastic cables 7. One end of the longitudinal elastic cable 7 is anchored at the node of the main beam 3, and the other end is anchored on the middle tower lower crossbeam 202. A lower crossbeam elastic cable pad 203 is set between the middle tower lower crossbeam 202 and the main beam 3. The elastic cables 7 pass through the lower crossbeam elastic cable pad 203, and the multiple elastic cables 7 are symmetrically arranged.

[0055] This application provides a design method for a longitudinal elastic cable constraint system, which is used to design the elastic cable constraint system of the above-mentioned kilometer-level three-tower cable-stayed bridge for both road and rail. It can solve the problem that the current methods for determining the cross-sectional area and length of the elastic cable involve multiple trial calculations, and that repeated trial calculations consume a lot of time and effort due to the complexity of the finite element model and the large number of element nodes.

[0056] The longitudinal elastic cable restraint system is designed using the following method:

[0057] 1. Determine the cross-sectional area of ​​the elastic cable

[0058] The longitudinal constraint of the central tower is set to fixed. Based on the longitudinal constraint force and the safety factor of the elastic cable structure under multiple stress conditions, multiple elastic cable cross-sectional areas are calculated. The maximum value of multiple elastic cable cross-sectional areas is taken as the design value of the elastic cable cross-sectional area.

[0059] Furthermore, according to formula A s =T / (μ×[σ s ]), calculate the cross-sectional area of ​​the elastic cable; where A s For the cross-sectional area of ​​the elastic cable, σ s Let T be the allowable stress value of the elastic cable, T be the longitudinal constraint force, and μ be the safety factor of the elastic cable structure.

[0060] Specifically, the longitudinal constraint of the central tower is set to fixed. The longitudinal constraint force T1 and the safety factor μ1 of the elastic cable structure under the main working condition are extracted. The longitudinal constraint force T2 and the safety factor μ2 of the elastic cable structure under the main working condition with additional loads are extracted. The longitudinal constraint force T3 and the safety factor μ3 of the elastic cable structure under the E2 seismic condition are extracted. These are then substituted with the allowable stress value [σs] of the elastic cable into formula A. s =T / (μ×[σ s ]), to obtain the cross-sectional area A of the elastic cable under the main working condition. s1The cross-sectional area A of the elastic cable under the main working condition is... s2 And the cross-sectional area A of the elastic cable under the E2 earthquake condition s3 Take A s =min(A s1 A s2 A s3 The cross-sectional area of ​​the elastic cable is determined by the value of , which serves as the design value for the area of ​​the elastic cable.

[0061] 2. Determine the length of the elastic cable

[0062] The cable length is determined based on the design value of the cross-sectional area of ​​the elastic cable and the maximum longitudinal displacement of the main beam.

[0063] Furthermore, by substituting the design value of the cross-sectional area of ​​the elastic cable and the initial cable length into the finite element model, the longitudinal displacement of the main beam under that cable length is calculated. It is then determined whether the longitudinal displacement of the main beam is less than or equal to the maximum longitudinal displacement of the main beam. If not, the cable length value is adjusted until the corresponding longitudinal displacement of the main beam is less than or equal to the maximum longitudinal displacement of the main beam, and the difference is minimized.

[0064] Specifically, the cable length is set as an integer multiple of the main beam section length; based on the determined elastic cable area A... s Initially proposed cable length L s0 Substituting the values ​​into the finite element model, the longitudinal displacement of the main beam under this cable length is calculated. Using the maximum longitudinal displacement of the main beam as a boundary constraint, it is determined whether the calculated longitudinal displacement is less than or equal to the maximum longitudinal displacement of the main beam. If not, the cable length is adjusted until the corresponding longitudinal displacement of the main beam is less than or equal to the maximum longitudinal displacement of the main beam, and the difference is minimized. That is, when the longitudinal displacement of the main beam corresponding to the proposed cable length is less than or equal to the maximum longitudinal displacement of the main beam, the longitudinal displacement of the main beam corresponding to a cable length close to this value is calculated. The difference between this cable length and the maximum longitudinal displacement of the main beam is compared, and the cable length corresponding to the longitudinal displacement of the main beam with the smallest difference is taken as the design value of the cable length. Only 3 to 4 trial calculations are needed to determine a reasonable cable length L. s .

[0065] Furthermore, after determining the cable length, the pretension of the elastic cable is determined based on the comprehensive reduction factor of the live load under normal operating conditions and the longitudinal constraint force generated by the live load under normal operating conditions when fixed with longitudinal constraints.

[0066] Specifically, according to formula F s =λT 活 Determine the pretension of the elastic cable; where F s T represents the pretension of the elastic cable, λ represents the comprehensive reduction factor for live load under normal operating conditions, and T represents the pretension of the elastic cable. 活 The longitudinal constraint force is the longitudinal constraint force generated by the live load under normal operating conditions when the longitudinal constraint is fixed.

[0067] By adopting the above technical solution, based on the longitudinal constraint force and the safety factor of the elastic cable structure under three working conditions when the longitudinal constraint of the central tower is set to fixed, and according to formula A s =T / (μ×[σ s The cross-sectional area of ​​the elastic cable for the three working conditions is calculated, and the maximum value is taken as the design value of the elastic cable cross-sectional area. That is, the cross-sectional area of ​​the elastic cable is determined first, and then the cable length is determined according to the design value of the elastic cable cross-sectional area and the maximum longitudinal displacement of the main beam. Since the cross-sectional area of ​​the elastic cable is already determined, only the cable length of the elastic cable needs to be calculated by trial calculation. Compared with the case where the cross-sectional area and the cable length of the elastic cable are uncertain, only 3 to 4 trial calculations are needed to determine the reasonable cable length L, which can greatly reduce the workload of trial calculation. This allows for the rapid and effective determination of the key parameters of the longitudinal elastic cable, creating favorable conditions for the subsequent detailed design of the bridge scheme.

[0068] On the other hand, this application also provides a cable-stayed bridge design method, including:

[0069] S1: Determine the span of the middle span, the height of the middle tower, the span of the side spans, and the height of the side towers.

[0070] Specifically, based on the navigation and flood control requirements of the waterway where the bridge is located, the two mid-span lengths L1 were determined.

[0071] Based on the angle of the outermost cable, the height of the side tower H1 and the height of the middle tower H2 are determined, and the span of the side span L2 is initially determined.

[0072] S2: Determine the parameters of the elastic cable restraint system between the central tower and the main beam.

[0073] 1. Determine the cross-sectional area of ​​the elastic cable

[0074] The longitudinal constraint of the central tower is set to fixed. Based on the longitudinal constraint force and the safety factor of the elastic cable structure under multiple stress conditions, multiple elastic cable cross-sectional areas are calculated. The maximum value of multiple elastic cable cross-sectional areas is taken as the design value of the elastic cable cross-sectional area.

[0075] Furthermore, according to formula A s =T / (μ×[σ s ]), calculate the cross-sectional area of ​​the elastic cable; where A s For the cross-sectional area of ​​the elastic cable, σ s Let T be the allowable stress value of the elastic cable, T be the longitudinal constraint force, and μ be the safety factor of the elastic cable structure.

[0076] Specifically, the longitudinal constraint of the central tower is set to fixed. The longitudinal constraint force T1 and the safety factor μ1 of the elastic cable structure under the main working condition are extracted. The longitudinal constraint force T2 and the safety factor μ2 of the elastic cable structure under the main working condition with additional loads are extracted. The longitudinal constraint force T3 and the safety factor μ3 of the elastic cable structure under the E2 seismic condition are extracted. These are then substituted with the allowable stress value [σs] of the elastic cable into formula A. s =T / (μ×[σ s ]), to obtain the cross-sectional area A of the elastic cable under the main working condition. s1 The cross-sectional area A of the elastic cable under the main working condition is... s2 And the cross-sectional area A of the elastic cable under the E2 earthquake condition s3 Take A s =min(A s1 A s2 A s3 The cross-sectional area of ​​the elastic cable is determined by the value of , which serves as the design value for the area of ​​the elastic cable.

[0077] 2. Determine the length of the elastic cable

[0078] The cable length is determined based on the design value of the cross-sectional area of ​​the elastic cable and the maximum longitudinal displacement of the main beam.

[0079] Furthermore, by substituting the design value of the cross-sectional area of ​​the elastic cable and the initial cable length into the finite element model, the longitudinal displacement of the main beam under that cable length is calculated. It is then determined whether the longitudinal displacement of the main beam is less than or equal to the maximum longitudinal displacement of the main beam. If not, the cable length value is adjusted until the corresponding longitudinal displacement of the main beam is less than or equal to the maximum longitudinal displacement of the main beam, and the difference is minimized.

[0080] Specifically, since the zero temperature point is located at the central tower, the length of the elastic cable is not affected by temperature stress, and can be kept as short as possible to save costs. At the same time, to reduce the expansion and contraction displacement at the beam ends, the length of the elastic cable should also be shorter. Considering the need for anchoring the elastic cable on the main beam, the cable length is set to an integer multiple of the main beam section length.

[0081] Based on the determined elastic cable area A s Initially proposed cable length L s0Substituting the values ​​into the finite element model, the longitudinal displacement of the main beam under this cable length is calculated. Using the maximum longitudinal displacement of the main beam as a boundary constraint, it is determined whether the calculated longitudinal displacement is less than or equal to the maximum longitudinal displacement of the main beam. If not, the cable length is adjusted until the corresponding longitudinal displacement of the main beam is less than or equal to the maximum longitudinal displacement of the main beam, and the difference is minimized. That is, when the longitudinal displacement of the main beam corresponding to the proposed cable length is less than or equal to the maximum longitudinal displacement of the main beam, the longitudinal displacement of the main beam corresponding to a cable length close to this value is calculated. The difference between this cable length and the maximum longitudinal displacement of the main beam is compared, and the cable length corresponding to the longitudinal displacement of the main beam with the smallest difference is taken as the design value of the cable length. Only 3 to 4 trial calculations are needed to determine a reasonable cable length L. s .

[0082] 3. Determine the pretension of the elastic cable.

[0083] After determining the cable length, the pretension of the elastic cable is determined based on the comprehensive reduction factor of the live load under normal operating conditions and the longitudinal constraint force generated by the live load under normal operating conditions when fixed with longitudinal constraints.

[0084] Specifically, according to formula F s =λT 活 Determine the pretension of the elastic cable; where F s T represents the pretension of the elastic cable, λ represents the comprehensive reduction factor for live load under normal operating conditions, and T represents the pretension of the elastic cable. 活 The longitudinal constraint force is the longitudinal constraint force generated by the live load under normal operating conditions when the longitudinal constraint is fixed.

[0085] S3: Determine the stiffness, bending moment, and spacing between the columns of the central tower.

[0086] To address the issues of low stiffness of the main beam (large vertical displacement) and large bending moment of the central tower, it is necessary to study a reasonable stiffness for the central tower.

[0087] The stiffness of the middle tower is determined based on the vertical displacement of the main beam; the bending moment of the middle tower is determined based on the stiffness of the middle tower.

[0088] Specifically, the stiffness of the central tower is determined according to the formula S = α1 × B, and the bending moment of the central tower is determined according to the formula M = α2 × B. Wherein, S is the vertical displacement of the main beam, α1 is the proportionality coefficient of the vertical displacement S of the main beam with the stiffness B of the central tower, B is the stiffness of the central tower, M is the bending moment of the central tower, and α2 is the proportionality coefficient of the bending moment M of the central tower with the stiffness B of the central tower. Both α1 and α2 are obtained through experiments.

[0089] Since the vertical displacement S of the main beam decreases as the stiffness B of the middle tower increases, and the bending moment M of the middle tower increases as the stiffness B of the middle tower increases, the vertical displacement limit [S], that is, the maximum vertical displacement of the main beam, can be determined to determine the stiffness B0 of the middle tower. At this time, the bending moment M of the middle tower is the minimum value within the allowable range.

[0090] After determining the stiffness of the middle tower, a finite element model of the middle tower is established. A longitudinal concentrated force P is applied to the top of the tower, and the longitudinal displacement Δ at the top of the tower is obtained. Then, the stiffness of the middle tower B' = Δ / P. By adjusting the spacing between the tower columns of the middle tower, multiple stiffness values ​​B' are obtained. Taking B' = B0, the optimal value S of the spacing between the tower columns of the middle tower can be determined. z .

[0091] S4: Determine the distance between the auxiliary pier and the side pier

[0092] Given the large beam end rotation angle θ, the distance L between the auxiliary pier and the side pier should be minimized as much as possible. a From the perspective of ensuring the safety factor K of the dike s Departure, L a It should be as large as possible. Establish the functional relationship: Beam end rotation angle θ = β1 × L a The safety factor of the embankment, Ks, is given by Ks = β2 × La, where β1 is the proportionality coefficient of the beam end rotation angle θ as a function of the distance La between the auxiliary pier and the side pier, and β2 is the proportionality coefficient of the embankment safety factor Ks as a function of the distance La between the auxiliary pier and the side pier. Both β1 and β2 are obtained experimentally. A graph of the two functional relationships is plotted, and their intersection point is taken as L. a Theoretical optimal solution L a0 Then, according to the relevant specifications for the limit value [θ] of the beam end rotation angle, the minimum distance [L] between the auxiliary pier and the embankment angle. d In the optimal solution L a0 Nearby L a value.

[0093] This embodiment has the following beneficial effects:

[0094] 1. It provides a guiding method for the design of a new type of kilometer-long dual-purpose (road and rail) three-tower cable-stayed bridge.

[0095] 2. The use of a longitudinal elastic cable restraint system solves the problem of large dynamic response of the bridge.

[0096] 3. To address the issues of the zero temperature point being located in the middle tower, large expansion and contraction displacement at the beam ends, and significant impact from live load, a method for determining the design values ​​of key parameters for the longitudinal elastic cable was established.

[0097] 4. To address the issues of low main beam stiffness and large bending moment in the middle tower, a reasonable method for determining the dimensions of the middle tower base is provided.

[0098] 5. In response to the problem of large angular displacement at the beam end and the impact of auxiliary piers on the safety of the embankment, a method for determining the reasonable distance between auxiliary piers and side piers is given.

[0099] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0100] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0101] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method of designing a longitudinal tendon restraint system, characterized by, The method comprises the following steps: The longitudinal constraint of the middle tower is set as fixed, and a plurality of elastic cable cross-sectional areas are calculated according to the longitudinal constraint forces under a plurality of stress conditions and the elastic cable structure safety factor, and the maximum value of the plurality of elastic cable cross-sectional areas is taken as the elastic cable cross-sectional area design value; The cable length is determined according to the elastic cable cross-sectional area design value and the maximum longitudinal displacement of the main beam; The method comprises the following steps: According to formula A s = T / (μ x [σ s ]), the elastic cable cross-sectional area is calculated; Wherein, A s is the elastic cable cross-sectional area, σ s is the elastic cable allowable stress value, T is the longitudinal restraint force, and μ is the elastic cable structure safety factor; The cable length is determined according to the elastic cable cross-sectional area design value and the maximum longitudinal displacement of the main beam; The cable length is adjusted until the corresponding longitudinal displacement of the main beam is less than or equal to the maximum longitudinal displacement of the main beam and the difference is minimum.

2. The design method of a longitudinal elastic cable-constrained architecture according to claim 1, characterized in that: The cable length is an integer multiple of the inter-span length of the main beam.

3. The design method of a longitudinal elastic cable-constrained architecture according to claim 1, characterized in that: After the cable length is determined, the pre-tension of the elastic cable is determined according to the comprehensive reduction coefficient of the live load under the normal operation state and the longitudinal constraint force generated by the live load under the normal operation state when the longitudinal constraint is fixed.

4. The design method of a longitudinal elastic cable-constrained system according to claim 3, wherein, The method comprises the following steps: According to the formula F s = λT 活 , the pre-tension of the elastic cable is determined; Wherein, F s is the pre-tension of the elastic cable, λ is the comprehensive reduction coefficient of live load in normal operation state, T 活 is the longitudinal constraint force generated by live load in normal operation state when fixed by longitudinal constraint.

5. A method of designing a cable-stayed bridge, characterized by, The method comprises the following steps: The midspan span, the middle tower height, the side span span and the side tower height are determined; The elastic cable constraint system parameters between the middle tower and the main beam are determined; The middle tower stiffness, the middle tower bending moment and the middle tower column spacing are determined; The distance between the auxiliary pier and the side pier is determined; The elastic cable constraint system parameters between the middle tower and the main beam are determined by the following steps: The longitudinal constraint of the middle tower is set as fixed, and a plurality of elastic cable cross-sectional areas are calculated according to the longitudinal constraint forces under a plurality of stress conditions and the elastic cable structure safety factor, and the maximum value of the plurality of elastic cable cross-sectional areas is taken as the elastic cable cross-sectional area design value; The cable length is determined according to the elastic cable cross-sectional area design value and the maximum longitudinal displacement of the main beam; The method comprises the following steps: According to formula A s = T / (μ x [σ s ]), the elastic cable cross-sectional area is calculated; Wherein, A s is the elastic cable cross-sectional area, σ s is the elastic cable allowable stress value, T is the longitudinal restraint force, and μ is the elastic cable structure safety factor; The cable length is determined according to the elastic cable cross-sectional area design value and the maximum longitudinal displacement of the main beam; The cable length is adjusted until the corresponding longitudinal displacement of the main beam is less than or equal to the maximum longitudinal displacement of the main beam and the difference is minimum.

6. The cable-stayed bridge design method according to claim 5, wherein The method comprises the following steps: The middle tower stiffness is determined according to the vertical displacement of the main beam; The middle tower bending moment is determined according to the middle tower stiffness.

7. The design method of a cable-stayed bridge according to claim 6, wherein The method comprises the following steps: The middle tower stiffness is determined according to the formula S=α1×B; The middle tower bending moment is determined according to the formula M=α2×B; Wherein, S is the vertical displacement of the main beam, B is the rigidity of the middle tower, M is the bending moment of the middle tower, α1 is the proportional coefficient of the vertical displacement of the main beam changing with the rigidity of the middle tower, and α2 is the proportional coefficient of the bending moment of the middle tower changing with the rigidity of the middle tower.

8. The design method of a cable-stayed bridge according to claim 7, characterized in that: According to the maximum vertical displacement of the main beam, the rigidity of the middle tower is determined, and according to the rigidity of the middle tower, the minimum bending moment of the middle tower is determined.

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