Calculation method of reasonable bridge completion state of cable-stayed bridge

Abstract

The present application relates to cable-stayed bridge technical field, especially a kind of calculation method of reasonable bridge completion state of cable-stayed bridge, catenary theory is used to calculate the unstressed cable length of cable, and is substituted into bridge completion state finite element model to carry out nonlinear calculation, the deformation value of tower and beam is calculated using finite element, and the anchor point coordinates of cable are corrected, then unstressed cable length is calculated again using catenary theory, and reasonable bridge completion state can be efficiently calculated by cyclic iteration calculation.

Description

A calculation method for the reasonable completed bridge state of a cable-stayed bridge Technical Field

[0001] This invention relates to the field of cable-stayed bridge technology, and in particular to a method for calculating the optimal completion state of a cable-stayed bridge. Background Technology

[0002] Cable-stayed bridges are highly statically indeterminate composite structural systems composed of three basic components: stay cables, towers, and stiffening girders. They have become one of the fastest-growing and most competitive bridge types in the world. The design process of cable-stayed bridges aims at achieving a reasonable completed bridge state, ensuring the following under the dead load of the completed bridge: (1) "Straight towers and level beams," meaning that the towers are vertical and the main beams are straight. (2) Reasonable distribution of cable force, meaning that the cable force increases basically uniformly with the cable length and has a sufficient safety factor. (3) Sufficient pressure reserve at the supports.

[0003] The cable forces of a cable-stayed bridge are a decisive factor in achieving the desired bridge completion state; therefore, solving for the desired bridge completion state can be transformed into a cable force optimization problem. Currently, there are many methods for optimizing cable forces in the completed state of cable-stayed bridges, such as the rigid-supported continuous beam method and the zero-displacement method. However, these methods all have errors in correcting the spatial coordinates of the upper and lower anchor points of the cables. Therefore, there is an urgent need for a calculation method for the desired bridge completion state of a cable-stayed bridge that can determine the spatial coordinates of the upper and lower anchor points of the cables. Summary of the Invention

[0004] This invention achieves the calculated target and constructs a reasonable bridge by correcting the spatial coordinates of the upper and lower anchor points of the stay cables twice and then fine-tuning the cable length once.

[0005] When a cable-stayed bridge is reasonably completed, as long as the external loads, structural system, support boundary conditions, and stress-free length and curvature of the elements are determined, the internal forces and alignment of the bridge in its final completed state after the dead load is completed are uniquely determined. Thus, the cable force optimization problem for cable-stayed bridges can be transformed into a stress-free cable length optimization problem. Based on this, this paper proposes a new method for calculating the reasonable completed state of cable-stayed bridges.

[0006] The specific method of the present invention is as follows: A method for calculating the reasonable completed state of a cable-stayed bridge, comprising the following steps:

[0007] Step 1: Obtain the vertical reaction force V1 of the elastic support and the stress-free cable length S1 of the stay cable;

[0008] Step 2: Substitute the stress-free cable length S1 into the finite model of the completed bridge for nonlinear calculation. At this time, both the tower and the beam undergo compressive deformation. During the geometric nonlinear analysis, the structure is in equilibrium after deformation. Extract the coordinates of the upper and lower anchor points of the cable to correct the compression deformation of the tower and the beam.

[0009] Step 3: After correcting the coordinates of the cable anchorage points by adjusting the compression of the tower and beam, the stress-free cable length S2 of the stay cable is calculated again using the vertical force V1 at the lower anchor point and the catenary 2-line equation.

[0010] Step 4: Substitute the stress-free cable length S2 into the finite element model of the completed bridge for nonlinear calculation again to extract the vertical deformation of the main beam;

[0011] Step 5: Multiply the vertical deformation of the main beam by the iterative correction coefficient λ, and then superimpose it onto the coordinates of the lower anchor point of the cable with the opposite sign. Calculate the stress-free cable length S3 again using the catenary theory, and take the vertical component force at the lower anchor point as V1. The iterative correction coefficient λ is determined through steps 5 and 6.

[0012] Step 6: Substitute the stress-free cable length S3 into the finite element model of the completed bridge for nonlinear calculation. By adjusting the value of the iteration correction coefficient λ in step 5, the finite element calculation of the completed bridge state is made close to the reasonable completed bridge state.

[0013] Step 7: Fine-tune the length of the stress-free cables in some of the stay cables to obtain a reasonable completed bridge state.

[0014] In step 1, the stay cables provide elastic constraints to the main beam, and a continuous beam model of the main beam with elastic support is established. The position of the stay cables is constrained by elastic support. The uniformity is adjusted according to the weight of the cable-supported beam segment. The adjusted V1 is input as a vertical force into the main beam model so that the main beam reaches a small deformation equilibrium state, and the vertical reaction force V1 of the elastic support under the dead load of the completed bridge is obtained.

[0015] When the stress-free cable length S1 is obtained, the origin of the stay cable is taken at the lower anchor point A. The tension at the lower anchor point is T1, with its horizontal component H1 and vertical component V1. The tension at any point (x, y) on the cable is T, with its horizontal component H and vertical component V. The horizontal distance between the upper and lower anchor points is a, and the angle between the line connecting the upper and lower anchor points and the horizontal direction is ω. cb The weight per unit length of the stay cable.

[0016] The catenary equation for a cable-stayed structure:

[0017] (1)

[0018] Its derivative equation is:

[0019] (2)

[0020] V1, H1, and T1 at point A satisfy the following conditions:

[0021] (3)

[0022] The equation for λ1 can be obtained as follows:

[0023] (4)

[0024] The equation was solved numerically using Newton's method, yielding λ1, the elongation of the stay cable:

[0025] (5)

[0026] Where E is the elastic modulus of the cable and A is the cross-sectional area of ​​the cable;

[0027] The stressed length of the stay cable:

[0028] (6)

[0029] The length of the stress-free cable of the stay cable:

[0030] (7)

[0031] In step 3, during the geometric nonlinear analysis, the structure reaches equilibrium after deformation, and the coordinates of the upper and lower anchor points of the cables are extracted to correct for the compression deformation of the tower and beam.

[0032] In step 4, since the tower, beam, and cable affect each other, the main beam will undergo a certain vertical deformation.

[0033] In step 5, the initial value of the iterative correction coefficient λ is between 1.0 and 2.0.

[0034] As can be seen from the above description, this scheme uses the catenary theory to calculate the stress-free cable length, and substitutes it into the finite element model of the completed bridge for nonlinear calculation. The finite element calculation of the tower and beam deformation values ​​is used to correct the coordinates of the cable anchor points, and then the catenary theory is used again to calculate the stress-free cable length. Through iterative calculation, a reasonable completed bridge state can be calculated efficiently. Attached Figure Description

[0035] Figure 1 is a diagram illustrating the theoretical calculation of the catenary of a cable-stayed bridge.

[0036] Figure 2 shows a model diagram of an elastically supported continuous beam.

[0037] Figure 3 shows a continuous beam model with V1 as the vertical force input.

[0038] Figure 4 is a flowchart of the present invention.

[0039] Figure 5 shows the bridge layout of (145+240+145)m.

[0040] Figure 6 is a schematic diagram of calculating the vertical support force V1 in the elastically supported continuous beam model.

[0041] Figure 7 is a schematic diagram of the deformation law of the main beam during the iteration process.

[0042] Figure 8 shows the cable force distribution of the completed cable-stayed bridge. Detailed Implementation

[0043] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the specific embodiments. The specific embodiments described are only one specific embodiment of the present invention, and not all specific embodiments.

[0044] As can be seen from the accompanying drawings, the method for calculating the reasonable completed state of a cable-stayed bridge according to the present invention includes the following steps:

[0045] Step 1: Obtain the vertical reaction force V1 of the elastic support and the stress-free cable length S1 of the stay cable;

[0046] The stay cables provide elastic constraints to the main girder, resulting in only minor deformation. At this point, the vertical component of the cable force is approximately equal to the dead load of the main girder. A continuous beam model with elastic support is established for the main girder, with the cable positions constrained by elastic supports. The vertical reaction force V1 of the elastic supports under the dead load of the completed bridge is calculated, as shown in Figure 2. V1 is not uniform at this point and needs to be adjusted for uniformity based on the weight of the cable-supported beam segment. The adjusted V1 is then input as a vertical force into the main girder model to achieve a small deformation equilibrium state in the main girder (see Figure 3). This V1 is a known condition for subsequent calculations.

[0047] As shown in Figure 1, the stress-free cable length iteration method gradually approximates the reasonable structure of a cable-stayed bridge through iteration of the stress-free cable length.

[0048] In bridge conditions, this method requires accurate calculation of the stress-free cable length. The cable length is calculated using the catenary theory. To obtain the stress-free cable length S1, the origin of the stay cable is taken at the lower anchor point A. The tension at the lower anchor point is T1, with its horizontal component H1 and vertical component V1. The tension at any point (x, y) on the cable is T, with its horizontal component H and vertical component V. The horizontal distance between the upper and lower anchor points is a, and the angle between the line connecting the upper and lower anchor points and the horizontal direction is ω. cb The weight per unit length of the stay cable.

[0049] The catenary equation for a cable-stayed structure:

[0050] (1)

[0051] Its derivative equation is:

[0052] (2)

[0053] V1, H1, and T1 at point A satisfy the following conditions:

[0054] (3)

[0055] The equation for λ1 can be obtained as follows:

[0056] (4) The equation is solved numerically using the Newton method to obtain λ1, the elongation of the cable:

[0057] (5)

[0058] Where E is the elastic modulus of the cable and A is the cross-sectional area of ​​the cable;

[0059] The stressed length of the stay cable:

[0060] (6)

[0061] The length of the stress-free cable of the stay cable:

[0062] (7)

[0063] Step 2: Substitute the stress-free cable length S1 into the finite model of the completed bridge for nonlinear calculation. At this time, both the tower and the beam undergo compressive deformation. During the geometric nonlinear analysis, the structure is in equilibrium after deformation. Extract the coordinates of the upper and lower anchor points of the cable to correct the compression deformation of the tower and the beam.

[0064] Step 3: After correcting the coordinates of the cable anchorage points by adjusting the compression of the tower and beam, the stress-free cable length S2 of the stay cable is calculated again using the vertical force V1 at the lower anchor point and the catenary equation.

[0065] Step 4: Substitute the stress-free cable length S2 into the completed bridge finite element model for nonlinear calculation again to extract the vertical deformation of the main beam; during the calculation of the completed bridge finite element model, since the tower, beam and cable are mutually influential, the main beam will undergo certain vertical deformation.

[0066] Step 5: Multiply the vertical deformation of the main beam by the iterative correction coefficient λ, and then superimpose it onto the coordinates of the lower anchor point of the cable with the opposite sign. Calculate the stress-free cable length S3 again using the catenary theory, and take the vertical component force at the lower anchor point as V1. The iterative correction coefficient λ is determined through steps 5 and 6. The initial value of the iterative correction coefficient λ is between 1.0 and 2.0.

[0067] Step 6: Substitute the stress-free cable length S3 into the finite element model of the completed bridge for nonlinear calculation. By adjusting the value of the iteration correction coefficient λ in step 5, the finite element calculation of the completed bridge state is made close to the reasonable completed bridge state.

[0068] Step 7: Fine-tune the length of the stress-free cables in some of the stay cables to obtain a reasonable completed bridge state.

[0069] The above method was applied to a (145+240+145)m central cable-stayed steel box girder bridge.

[0070] The bridge is a (145+240+145)m central cable-stayed steel box girder bridge with a fixed tower-girder structure and separate piers and beams. The main girder is a steel box girder with a height of 4.8m and a total width of 28.5m. The towers are steel cable towers with a height of 57m above the bridge deck. The stay cables are high-strength parallel steel wire stay cables, with 18 pairs of stay cables on each tower. There are a total of 72 stay cables on the bridge. The stay cables are numbered from shortest to longest in the side spans as S1 to S9, and from shortest to longest in the middle spans as M1 to M9, as shown in Figure 5.

[0071] After calculating the vertical force and adjusting for uniformity in the elastically supported continuous beam model, part V1 is shown in Figure 6. At this time, the maximum deformation value of the elastically supported continuous beam is 7.2 mm.

[0072] Following the calculation steps outlined above, the stress-free cable lengths S1, S2, and S3 were calculated and fine-tuned. In step 2, the stress-free cable length was calculated using MATLAB numerically based on catenary theory. In step 6, the iteration correction coefficient λ was set to 1.5. Through iterative iteration and fine-tuning, the main beam displacement gradually approached zero during the entire iteration process. The final state showed a mid-span deformation of approximately -8mm, while the side spans near the piers experienced slightly larger deformations (approximately -17mm) due to the lack of cable support. The overall bridge alignment of the main beam was considered reasonable, as shown in Figure 7. The cable forces in the completed bridge state are shown in Figure 8. Shorter cables exhibited smaller forces, while longer cables showed larger forces, and the force distribution was uniform.

[0073] Analysis of the calculation results of this bridge shows that the stress-free cable-stayed bridge long iteration method can quickly and accurately calculate the reasonable bridge completion state of a cable-stayed bridge in just a few steps. The mechanical concepts are clear, the steps are simple and efficient, and the operation is strong.

[0074] As can be seen from the above description, in this invention: 1. The stay cables act as elastic supports for the main beam, and their vertical force components at the beam ends balance the vertical load of the main beam. Starting from this basic mechanical model, the catenary theory is used to calculate the stress-free cable length, which is then substituted into the finite element model of the completed bridge for nonlinear calculation. The deformation results of the finite element calculation correct the coordinates of the cable anchor points, and then the catenary theory is used again to calculate the stress-free cable length. Through multiple iterative calculations, a reasonable completed bridge state can be efficiently calculated. Engineering examples verify that the stress-free cable length iteration method can accurately calculate the reasonable completed bridge state of a cable-stayed bridge. The mechanical concepts are clear, the steps are simple and efficient, and the operation is strong. It is also applicable to asymmetric structures. 2. The stress-free cable length iteration method adopts the idea of ​​"disassembling before assembling" the structure. It first disassembles the structure into components such as the main beam and cables, and then assembles the overall structure of the cable-stayed bridge. The stress balance and deformation coordination of the structure play a related role between the components and the structure. This calculation method involves three models, two corrections, and one adjustment; the three models are: the elastic support continuous beam model, the catenary method for calculating the stress-free cable length, etc.

[0075] The analysis model and the finite element model of the completed bridge were used. Two corrections were made: one for the compression of the upper and lower anchor points and the other for the vertical displacement of the main beam. One adjustment was made for the fine-tuning of the stress-free cable length. 3. The completed bridge state calculated using the stress-free cable length iteration method transforms the solution for cable force into the solution for stress-free cable length. The resulting reasonable completed bridge state can be directly used to calculate the reasonable construction stage based on the stress-free state control method proposed by Academician Qin Shunquan. The principle of the stress-free state control method is that for a structure composed of a given external load, structural system, support boundary conditions, stress-free element length, and stress-free curvature, the corresponding internal forces and displacements are unique and independent of the structure's formation process.

[0076] The above are specific embodiments of the present invention. For those skilled in the art, it will be understood that various changes, modifications, substitutions and variations can be made to these specific embodiments without departing from the principles and spirit of the invention, and all such changes and variations are within the protection scope of the present invention.

Claims

1. A method for calculating the reasonable completed bridge state of a cable-stayed bridge, characterized in that... The process includes the following steps: Step 1: Obtain the vertical support reaction force V1 and the stress-free cable length S1 of the stay cable; Step 2: Substitute the stress-free cable length S1 into the finite element model of the completed bridge for nonlinear calculation, during which both the tower and the beam undergo compression deformation; Step 3: After correcting the coordinates of the cable anchorage points based on the compression of the tower and beam, calculate the stress-free cable length S2 of the stay cable again using the vertical force V1 at the lower anchorage and the catenary equation; Step 4: Substitute the stress-free cable length S2 into the finite element model of the completed bridge for nonlinear calculation again, extracting the vertical deformation of the main beam; Step 5: Multiply the vertical deformation of the main beam by the iteration correction coefficient λ, then superimpose it onto the coordinates of the lower anchorage of the stay cable with the opposite sign, and calculate the stress-free cable length S3 again using the catenary theory, taking V1 as the vertical component of the lower anchorage; the iteration correction coefficient λ is determined through steps 5 and 6; Step 6: Substitute the stress-free cable length S3 into the finite element model of the completed bridge for nonlinear calculation, adjusting the iteration coefficient λ in step 5... The value of the correction coefficient λ is adjusted to make the finite element calculation of the bridge state close to the reasonable bridge state; Step 7: Fine-tune the length of the stress-free cable of some stay cables to obtain the reasonable bridge state; In step 1, the stay cables provide elastic constraints for the main beam, and a continuous beam model of the main beam with elastic support is established. The cable position is constrained by elastic support. The uniformity is adjusted according to the weight of the cable support beam segment. The adjusted V1 is input as a vertical force into the main beam model so that the main beam reaches a small deformation equilibrium state, and the vertical reaction force V1 of the elastic support under the dead load of the completed bridge is obtained; When the stress-free cable length S1 is obtained, the origin of the stay cable is taken at the lower anchor point A, the tension at the lower anchor point of the stay cable is T1, its horizontal component is H1, and its vertical component is V1; the tension at any point (x,y) on the cable is T, its horizontal component is H, and its vertical component is V, the horizontal distance between the upper and lower anchor points is a, and the angle between the line connecting the upper and lower anchor points and the horizontal direction is ω, g cb Given the weight per unit length of the stay cable, the equation for the catenary of the stay cable structure is: (1) Its derivative equation is: (2) V1, H1, and T1 at point A satisfy the following conditions: (3) The equation for λ1 can be obtained: (4) The equation is solved numerically using the Newton method to obtain λ1, the elongation of the cable: (5) Where E is the elastic modulus of the cable, and A is the cross-sectional area of ​​the cable; the stress length of the cable is: (6) Length of the stress-free cable of the stay cable: （7） 2. The calculation method for the reasonable completed bridge state of a cable-stayed bridge according to claim 1, characterized in that: In step 3, during the geometric nonlinear analysis, the structure reaches equilibrium after deformation, and the coordinates of the upper and lower anchor points of the cables are extracted to correct for the compression deformation of the tower and beam.

3. The calculation method for the reasonable completed bridge state of a cable-stayed bridge according to claim 2, characterized in that: In step 4, since the tower, beam, and cable affect each other, the main beam will undergo a certain vertical deformation.

4. The calculation method for the reasonable completed bridge state of a cable-stayed bridge according to claim 3, characterized in that: In step 5, the initial value of the iterative correction coefficient λ is between 1.0 and 2.0.

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