A method for designing proportion of loads of each arch ring in a process of forming arches by arch rings of a stiff skeleton concrete arch bridge

Abstract

The application discloses a design method for load sharing ratio of each arch ring in a process of arch forming by rings of a stiff skeleton concrete arch bridge, and relates to the technical field of bridge engineering. The method comprises the following steps: setting a calculation assumption condition; deducing a calculation relation of load sharing ratio of each bearing unit based on the principle of structural mechanics; and obtaining the load sharing ratio of each bearing unit through the calculation relation in combination with mechanical parameters of the bearing units. The application realizes automation of the calculation process, reduces manual intervention, and improves calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, and more specifically to a method for designing the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge. Background Technology

[0002] Due to its advantages such as high rigidity, beautiful appearance, strong adaptability to mountainous areas and low maintenance cost, the rigid frame concrete arch bridge has become one of the core bridge types for long-span mountainous bridges.

[0003] In the construction of this type of bridge, the concrete surrounding the main arch ring is often poured using a segmented ring method, which results in the asynchronous formation of the cross-sectional stiffness with each construction stage. The stress development process of each component differs significantly, the material's time-varying characteristics are complex, and the control of the arch formation state is extremely difficult.

[0004] Accurately determining the load-sharing ratio of each arch ring (stiffening frame, inner tube concrete, bottom slab concrete, web concrete, top slab concrete, etc.) during the arch formation process is crucial for ensuring construction safety and optimizing structural design. Current technologies rely heavily on engineering experience or complex finite element simulations to calculate the load-sharing ratio of each arch ring, which has the following drawbacks: First, the empirical method lacks accuracy and is difficult to adapt to the complex stress conditions of long-span bridges; second, finite element simulations are labor-intensive, inefficient, and require highly skilled operators; and third, the lack of a unified and universal theoretical calculation method leads to poor comparability of calculation results across different projects, making it difficult to establish standardized design guidelines.

[0005] Therefore, proposing a design method for the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge to solve the difficulties existing in the prior art is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a method for designing the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge, in order to solve the problems of complex calculations, insufficient accuracy, and reliance on experience in the prior art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A method for designing the load distribution ratio of each arch ring during the segmented arch construction process of a reinforced concrete arch bridge includes the following steps: S1. Set the calculation assumptions; S2. Based on the principles of structural mechanics, derive the calculation relationship of the load sharing ratio of each load-bearing unit; S3. Combining the mechanical parameters of each load-bearing unit, the load-sharing ratio of each load-bearing unit is obtained through calculation.

[0008] Optionally, the assumptions in S1 include material property assumptions, deformation state assumptions, and displacement compatibility assumptions.

[0009] Optionally, the load-bearing unit in S2 includes a stiffening frame and concrete rings.

[0010] Optionally, the concrete of each ring includes a bottom slab concrete arch ring, a web concrete arch ring, and a top slab concrete arch ring.

[0011] Optionally, the specific details of the calculation assumptions in S1 are as follows: Material homogeneity assumption: Concrete and steel are uniformly distributed in the longitudinal direction and are both isotropic materials; Small deformation assumption: The arch structure does not undergo large deformation during construction, and the stress-strain relationship of the material is within the linear elastic range; Displacement compatibility assumption: No relative displacement occurs between the stiffening frame and the concrete of each ring; The arch axis approximation assumption is that the arch axis of the stiffening frame and each ring of concrete has the same shape and length, and there is only a vertical offset.

[0012] Optionally, the structural mechanics principle in S2 is the principle of virtual work, and the derivation process of the calculation relationship is as follows: Formula for calculating elastic displacement of an arch structure: , in, To simulate the internal forces in the structure caused by a unit load, The internal forces of the structure caused by the actual load. The elastic modulus of the material. The moment of inertia of the cross section is the bending moment. The length of the infinitesimal element of the arch axis; The loads shared by the stiffening frame and the concrete of each ring are as follows: Total load The displacement of each arch ring is denoted as .

[0013] Optionally, the mechanical parameters in S3 include the elastic modulus of the material of each load-bearing element and the moment of inertia relative to the neutral axis of the composite section. The formula for calculating the load distribution ratio is as follows: ,in, This represents the number of load-bearing units that have been joined together. For the first i The load-sharing ratio of each load-bearing unit and They represent the first i and the j The elastic modulus of the arch material and They represent the first i and the j The moment of inertia of each arch ring relative to the neutral axis of the composite section.

[0014] Optionally, it also includes the step of deriving a simplified calculation formula for the load-sharing ratio based on the structural displacement increment: Define displacement parameters: Let Deformation of the rigid frame arch under a unit load before concrete pouring; For the first i The increase in arch crown deformation of the main arch structure under a unit load when the ring concrete has just been poured; Derivation of the simplified formula for load sharing ratio: i The first bearing unit undertakes the first i The proportion of +1 ring concrete self-weight is based on calculate; Calculate the total load-sharing ratio: Let the first... i The proportion of the weight of the +1 ring concrete to the weight of the arch box is: Then the first i The proportion of the total load borne by each bearing unit is: .

[0015] Optional, deformation increment The data can be obtained through actual measurements using a structural displacement monitoring device or through calculations using a finite element model.

[0016] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for designing the load distribution ratio of each arch ring in the process of constructing a rigid frame concrete arch bridge, the beneficial effects of which are: 1) This invention derives the load-sharing ratio calculation relationship based on the core principles of structural mechanics, and combines scientific assumptions to ensure rigorous calculation logic and reliable results, thus solving the problem of insufficient accuracy of traditional empirical methods; 2) It provides two calculation paths: accurate calculation and simplified calculation. The accurate formula meets the high-precision design requirements, while the simplified formula is easy to apply quickly on the engineering site, balancing accuracy and practicality. 3) The mechanical parameter requirements of each arch ring are clearly defined, and the calculation process is standardized and regulated, which can be widely applied to stiffened frame concrete arch bridges with different spans and structural forms, and has strong versatility; 4) The load distribution system designed in conjunction with the bridge automates the calculation process, reduces manual intervention, improves calculation efficiency, and provides accurate data support for bridge construction scheme optimization, stress control and safety assessment, which helps to promote the development of stiffened frame concrete arch bridges towards larger spans and higher quality. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 A flowchart of a method for designing the load distribution ratio of each arch ring in the process of constructing a rigid frame concrete arch bridge, provided by the present invention. Figure 2 A diagram illustrating the ring-splitting method of the arch ring is provided for this invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] See Figure 1 As shown, this invention discloses a method for designing the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge, including the following steps: S1. Set the calculation assumptions; S2. Based on the principles of structural mechanics, derive the calculation relationship of the load sharing ratio of each load-bearing unit; S3. Combining the mechanical parameters of each load-bearing unit, the load-sharing ratio of each load-bearing unit is obtained through calculation.

[0021] Furthermore, the assumptions in S1 include material property assumptions, deformation state assumptions, and displacement compatibility assumptions.

[0022] Furthermore, the load-bearing unit in S2 includes a stiffening frame and concrete rings.

[0023] Furthermore, the concrete of each ring includes the bottom slab concrete arch ring, the web concrete arch ring, and the top slab concrete arch ring.

[0024] Furthermore, the specific details of the assumptions calculated in S1 are as follows: Material homogeneity assumption: Concrete and steel are uniformly distributed in the longitudinal direction and are both isotropic materials; Small deformation assumption: The arch structure does not undergo large deformation during construction, and the stress-strain relationship of the material is within the linear elastic range; Displacement compatibility assumption: No relative displacement occurs between the stiffening frame and the concrete of each ring; The arch axis approximation assumption is that the arch axis of the stiffening frame and each ring of concrete has the same shape and length, and there is only a vertical offset.

[0025] Specifically, based on the above assumptions, the stiffening frame and the concrete of each ring can be simplified into ordinary arch structures in the longitudinal direction. The arch axis shapes of each arch are approximately the same, with slight differences in the length of the arch axis. Taking the stiffening frame and the bottom slab concrete as an example, if we assume the difference in length between one side of the two arches is , then we have:

[0026] In the formula, This refers to the distance between the two arches, specifically the distance between the axis of the concrete arch in the base slab and the axis of the rigid frame arch. The arch's height; The span of the arch.

[0027] because The value of is often small, and its proportion to the span of the arch structure is even smaller; for long-span arch bridges, the rise-to-span ratio is also very small, so it can be ignored. The calculation assumes that the arch axes of the stiffening frame and each ring of concrete are not only the same in shape, but also equal in length, with only a certain distance offset in the vertical direction.

[0028] Furthermore, the structural mechanics principle in S2 is the principle of virtual work, and the derivation process of the calculation relationship is as follows: Formula for calculating elastic displacement of an arch structure: , in, To simulate the internal forces in the structure caused by a unit load, The internal forces of the structure caused by the actual load. The elastic modulus of the material. The moment of inertia of the cross section is the bending moment. The length of the infinitesimal element of the arch axis; The loads shared by the stiffening frame and the concrete of each ring are as follows: Total load The displacement of each arch ring is denoted as .

[0029] Furthermore, the mechanical parameters in S3 include the elastic modulus of the material of each load-bearing element and the moment of inertia relative to the neutral axis of the composite section. The formula for calculating the load distribution ratio is as follows: ,in, This represents the number of load-bearing units that have been joined together. For the first i The load-sharing ratio of each load-bearing unit and They represent the first i and the j The elastic modulus of the arch material and They represent the first i and the j The moment of inertia of each arch ring relative to the neutral axis of the composite section.

[0030] Specifically, when a load P is applied to the arch structure, the formula is... It can be simplified to:

[0031] Assuming the moment of inertia of the cross-section of the structure along the arch axis remains constant, the above equation can be rewritten as:

[0032] in, .

[0033] Under load P, the loads shared by the stiffening frame and the concrete of each ring are respectively... Total load The displacement of each arch ring is denoted as According to the formula have:

[0034] In the formula, Regarding the material modulus of each arch ring, it should be specifically noted that... This refers to the moment of inertia of each arch ring relative to the neutral axis of the composite section, rather than the moment of inertia relative to the neutral axis of the individual arch ring sections. This represents the number of load-bearing units that have already been joined together.

[0035] Although the elastic modulus and bending moment of inertia of the materials of each arch ring are different, since the structural form of each arch ring is the same, within the elastic range of the materials, let them be respectively composed of The bending moments at any cross section generated by the load are respectively Then we have:

[0036] For the same structural form They are the same, therefore:

[0037] Because the main arch ring is constructed symmetrically from left to right, the various arch rings do not experience lateral relative displacement, nor do they separate vertically. Therefore: ; Summarized as follows:

[0038] Therefore, the first i The load proportion borne by each arch ring is: .

[0039] Furthermore, it also includes the step of deriving a simplified calculation formula for the load-sharing ratio based on the structural displacement increment: Define displacement parameters: Let Deformation of the rigid frame arch under a unit load before concrete pouring; For the first i The increase in arch crown deformation of the main arch structure under a unit load when the ring concrete has just been poured; Derivation of the simplified formula for load sharing ratio: i The first bearing unit undertakes the first i The proportion of +1 ring concrete self-weight is based on calculate; Calculate the total load-sharing ratio: Let the first... i The proportion of the weight of the +1 ring concrete to the weight of the arch box is: Then the first i The proportion of the total load borne by each bearing unit is: .

[0040] Specifically, as concrete is poured, the neutral axis of the cross section in the composite structure changes continuously, which makes the calculation of the bending moment of inertia complex and requires repeated calculations based on the number of construction stages. Therefore, in order to better serve the needs of the project, a simplified calculation formula with an accuracy acceptable to the project is proposed.

[0041] set up The deformation of the rigid frame arch under a unit load before concrete pouring; Indicates the first i When the ring concrete is just poured, the increase in arch crown deformation of the main arch structure under a unit load can be expressed as: The proportion of the weight of the first ring concrete borne by the stiffening frame can be expressed as: Since the concrete of the first ring has just been poured and its strength has not yet been formed, its self-weight load is entirely borne by the stiffening frame, and there is Therefore, , .

[0042] Now consider the proportion of the self-weight of the second ring concrete borne by each arch ring after the second ring concrete is poured. This is the increase in deformation of the arch crown under a unit load immediately after the second ring of concrete is poured. At this point, the first ring of concrete has already formed an integral part with the stiffening frame, while the second ring of concrete has not yet participated in the combined action. Therefore, the proportions of the self-weight load of the second ring of concrete borne by the stiffening frame and the first ring of concrete are:

[0043] And so on, It was beforei When the three arches work together, the first i The first arch bears the first i +1 ring concrete self-weight ratio, if the first ring concrete self-weight ratio is increased by 1 / 2, if the first ring concrete i The proportion of the weight of the +1 ring concrete to the weight of the arch box is denoted as: Then the first i The proportion of load borne by each arch ring is: .

[0044] Furthermore, the deformation increment The data can be obtained through actual measurements using a structural displacement monitoring device or through calculations using a finite element model.

[0045] In one specific embodiment, for a reinforced concrete structure with a span of 138m, the proportion of the load borne by the arch ring during the segmented casting of the main arch ring concrete of the hingeless arch was calculated.

[0046] The main arch of the bridge has a single-box, three-cell cross-section, and the main arch concrete was poured using a four-ring, six-working-face method, with the rings arranged as follows: Figure 2 As shown. The first ring consists of 1.5m high concrete for the bottom slab and web of the side chamber; the second ring consists of the top slab of the side chamber and the remaining 1.3m high concrete for the web; the third ring consists of the bottom slab of the intermediate chamber; and the last ring consists of the top slab of the intermediate chamber. The first and second rings are poured using six working faces, while the third and fourth rings are poured continuously in one go.

[0047] When using a simplified calculation formula to solve for the proportion of the unreinforced concrete self-weight load shared by each arch ring, the bending moment of inertia corresponding to each arch ring can be obtained through the knowledge of structural mechanics. The final arch ring load sharing ratio is shown in Table 1. It should be noted that only the proportion of the concrete self-weight load of each ring in the steel frame was calculated. Therefore, only this parameter is compared in Table 1.

[0048] Table 1. Results of Load Distribution Ratio for Each Arch Ring

[0049] As shown in Table 1, the maximum error between the load distribution ratio of the arch rings calculated by the simplified method at different construction stages and the measured results is 4.5%, which is within the acceptable error range in engineering. This verifies the correctness of the simplified calculation formula for the load distribution ratio of each arch ring in a rigid frame concrete arch bridge.

[0050] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0051] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. 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 the invention. Therefore, the invention 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 disclosed herein.

Claims

1. A method for designing the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge, characterized in that, Includes the following steps: S1. Set the calculation assumptions; S2. Based on the principles of structural mechanics, derive the calculation relationship of the load sharing ratio of each load-bearing unit; S3. Combining the mechanical parameters of each load-bearing unit, the load-sharing ratio of each load-bearing unit is obtained through calculation.

2. The method for designing the load-sharing ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge according to claim 1, characterized in that, The assumptions in S1 include material property assumptions, deformation state assumptions, and displacement compatibility assumptions.

3. The method for designing the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge according to claim 1, characterized in that, The load-bearing unit in S2 includes a stiffening frame and concrete rings.

4. The method for designing the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge according to claim 3, characterized in that, The concrete of each ring includes the bottom slab concrete arch ring, the web concrete arch ring, and the top slab concrete arch ring.

5. The method for designing the load-sharing ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge according to claim 1, characterized in that, The specific details of the calculation assumptions in S1 are as follows: Material homogeneity assumption: Concrete and steel are uniformly distributed in the longitudinal direction and are both isotropic materials; Small deformation assumption: The arch structure does not undergo large deformation during construction, and the stress-strain relationship of the material is within the linear elastic range; Displacement compatibility assumption: No relative displacement occurs between the stiffening frame and the concrete of each ring; The arch axis approximation assumption is that the arch axis of the stiffening frame and each ring of concrete has the same shape and length, and there is only a vertical offset.

6. The method for designing the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge according to claim 1, characterized in that, The structural mechanics principle in S2 is the principle of virtual work. The derivation process of the calculation relationship is as follows: Formula for calculating elastic displacement of an arch structure: , in, To simulate the internal forces in the structure caused by a unit load, The internal forces of the structure caused by the actual load. The elastic modulus of the material. The bending moment of inertia of the cross section, The length of the infinitesimal element of the arch axis; The loads shared by the stiffening frame and the concrete of each ring are as follows: Total load The displacement of each arch ring is denoted as .

7. The method for designing the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge according to claim 1, characterized in that, The mechanical parameters in S3 include the elastic modulus of the material of each load-bearing element and the moment of inertia relative to the neutral axis of the composite section. The formula for calculating the load distribution ratio is as follows: ,in, This represents the number of load-bearing units that have been joined together. For the first i The load-sharing ratio of each load-bearing unit and They represent the first i and the j The elastic modulus of the arch material and They represent the first i and the j The moment of inertia of each arch ring relative to the neutral axis of the composite section.

8. The method for designing the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge according to claim 1, characterized in that, It also includes the step of deriving a simplified calculation formula for the load-sharing ratio based on the structural displacement increment: Define displacement parameters: Let Deformation of the rigid frame arch under a unit load before concrete pouring; For the first i The increase in arch crown deformation of the main arch structure under a unit load when the ring concrete has just been poured; Derivation of the simplified formula for load sharing ratio: i The first bearing unit undertakes the first i The proportion of +1 ring concrete self-weight is based on calculate; Calculate the total load-sharing ratio: Let the first... i The proportion of the weight of the +1 ring concrete to the weight of the arch box is: Then the first i The proportion of the total load borne by each bearing unit is: .

9. The method for designing the load distribution ratio of each arch ring during the segmented arch formation process of a rigid frame concrete arch bridge according to claim 8, characterized in that, Deformation increment The data can be obtained through actual measurements using a structural displacement monitoring device or through calculations using a finite element model.

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