A bridge deck continuous structure calculation analysis method suitable for a support arrangement form of RHHR

Abstract

The application discloses a bridge deck continuous structure calculation analysis method suitable for a RHHR support arrangement form, relates to the field of bridge engineering, and comprises the following steps: a macro mechanics model is established; in the RHHR support arrangement form, the load is symmetrically arranged, a half structure is analyzed, the unbonded connecting plate is disconnected from the middle, and a roller support is additionally arranged in the middle of the unbonded connecting plate and used for constraining the bending moment and the longitudinal bridge direction freedom and releasing the vertical freedom, wherein, R represents a sliding support, and H represents a hinged support. The macro mechanics model established by the application can be used in cooperation with a plane beam unit, the influence of material nonlinearity in the structure can be considered at the same time while the calculation efficiency is greatly improved, and the calculation precision is ensured.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering, specifically to a calculation and analysis method for continuous bridge deck structures under RHHR bearing arrangement. This model can take into account the influence of different bearing arrangements on the stress of the continuous bridge deck structure. Background Technology

[0002] Simply supported bridges frequently experience end corrosion. This problem primarily stems from water leakage and seepage at expansion joints, as well as the intrusion of harmful media. To reduce maintenance and repair costs, the concept of expansion joint-free bridges has emerged. This innovative design aims to eliminate expansion joints while maintaining the continuity and integrity of the bridge deck. The section of the bridge deck connecting two adjacent bridges is called a connecting plate. In bridge repair projects, to mitigate the impact of adding connecting plates on existing simply supported beams and to reduce tensile stress within the connecting plates to prevent crack propagation, a common practice is to debond the connecting plate from the beam structure. This involves placing a low-friction isolation layer, such as..., between the connecting plate and the underlying precast beam segment. Figure 1 As shown.

[0003] In the continuous reconstruction of simply supported bridge decks, the uncertain bearing arrangement of the original simply supported beam bridges leads to various bearing arrangements for the continuous bridge deck structure after the addition of connecting plates between adjacent simply supported beam bridges. If "R" represents a sliding bearing and "H" represents a hinged bearing, the possible bearing arrangements for the continuous bridge deck structure include: RHHR, HRRH, etc. Figure 2 As shown.

[0004] Studies have shown that different support arrangements have a significant impact on the stress on continuous bridge deck structures. Existing computational analysis methods mainly fall into two categories: refined finite element simulation and simplified analysis models. Refined finite element analysis requires extensive modeling work, and if material nonlinearity and geometric nonlinearity are to be considered in the computational analysis, iterative calculations are unavoidable, increasing computation time and potentially leading to non-convergence. While simplified analysis models can roughly simulate the stress and deformation of continuous bridge deck structures, they cannot consider material nonlinearities in beam segments other than connecting plates, resulting in decreased computational accuracy. Summary of the Invention

[0005] To address the problems existing in the prior art, the present invention aims to provide a calculation and analysis method for continuous bridge deck structures under RHHR support arrangement. This model is applicable to the calculation and analysis of continuous bridge deck structures, can consider the influence of different support arrangement forms, and can be used to guide the design of this type of bridge. This macroscopic mechanical model can be used in conjunction with planar beam elements, which can significantly improve calculation efficiency while simultaneously considering the influence of material nonlinearity in the structure, thus ensuring calculation accuracy.

[0006] To further achieve the above objectives, the present invention adopts the following technical solution: A calculation and analysis method for bridge deck continuous structures applicable to the RHHR bearing arrangement includes establishing a macroscopic mechanical model: under the RHHR bearing arrangement, assuming symmetrical load arrangement, half-structure analysis is performed, the unbonded connecting plate is broken in the middle, and a roller bearing is added in the middle of the unbonded connecting plate to constrain the bending moment and longitudinal bridge degree of freedom, and release the vertical degree of freedom, where R represents a sliding bearing and H represents a hinged bearing.

[0007] Furthermore, the governing equations of the macroscopic mechanical model are: (16), In the formula, These are the displacement increment vector and the force increment vector, respectively. This is the tangent stiffness matrix of the macroscopic mechanical model.

[0008] Furthermore, the derivation process of the governing equations of the macroscopic mechanical model includes: Under the action of external load, the beam end rotated. The elongation of the reinforcing bars in the unbonded joint plate Represented as: (1), In the formula, It is the distance between the neutral axis of the composite section and the neutral axis of the connecting plate; It is the distance between the neutral axis of the composite section and the central axis of the concrete beam section; It is the height of the neutral axis of the concrete beam; This refers to the rotation angle of the concrete beam at the support position; At this moment, the tension in the connecting plate Calculate according to the following formula: (2), In the formula, For the transition interface and support spacing; The distance between the support and the end of the concrete beam; The distance from the end of the concrete beam to the center of the connecting plate; and These are the elastic modulus and cross-sectional area of ​​the reinforcing bars in the connecting plate, respectively. Bending moment at the interface between the connecting plate and the composite beam segment and the bending moment borne by the virtual rigid arm at the contact point. Represented as: (3), (4), In the formula, It is the bending stiffness of the connecting plate; and These refer to the corners of the transition interface and the contact point, respectively. and These represent the vertical displacements of the transition interface and the contact point, respectively. Shear force at the transition interface Contact force at the contact point Represented as: (5), (6), Bending moment at transition section The bending moment borne by the virtual rigid arm above the hinge support Represented as: (7), (8), In the formula, It refers to the flexural stiffness of a concrete beam; Shear force at the transition interface Contact force at the contact point Represented as: (9), (10), Bending moment at the transition interface and shear force Represented as: (11), (12), Furthermore, the moment equilibrium condition at the virtual rigid arm is: (13), (14), The force equilibrium condition at the point of contact is: (15), Solve the equations (11)-(15) simultaneously and perform differentiation to obtain the governing equation (16) of the macroscopic mechanical model.

[0009] Furthermore, the aforementioned , , , Calculate according to the following formulas: (17), (18), (19), (20).

[0010] Compared with the prior art, the present invention has at least the following beneficial effects: The macroscopic mechanical model proposed in the present invention can: (a) Consider the influence of support arrangement; (b) The response of the bridge deck continuous structure can be obtained by solving the governing equations, and it can be used with planar beam elements. Compared with spatial finite element models (three-dimensional solid elements), it has high computational efficiency. (c) The macroscopic mechanical model of the present invention can be used in conjunction with planar beam elements. In planar beam elements, the influence of material nonlinearity can be considered, which can improve the calculation accuracy compared with the simplified analysis model. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the continuous bridge deck structure. Figure 2 This is a schematic diagram of different support arrangements for a continuous bridge deck structure. In the diagram, L represents the span of a simply supported beam (support spacing). Figure 3 A schematic diagram of the support reaction force under the RHHR support arrangement; Figure 4 The stress and deformation of the transition section of the bridge deck continuous structure under the RHHR support arrangement; Figure 5 This is a schematic diagram of section II of the transition section under the RHHR support arrangement. Figure 6 The stress and deformation of the connecting plate under the RHHR support arrangement; Figure 7 The stress and deformation of the beam segment below the connecting plate under the RHHR support arrangement; Figure 8 The stress and deformation at the transition interface between the simply supported beam segment and the connecting plate in the RHHR support arrangement; Figure 9 This is a schematic diagram of finite element modeling for a planar beam with RHHR support arrangement, using a macroscopic mechanical model. Figure 10 A schematic diagram of a bridge deck continuous structure with RHHR support arrangement; Figure 11 The mid-span deflection is calculated using a macroscopic mechanical model and planar beam elements under the RHHR support arrangement.

[0012] In the diagram: L represents the span of the simply supported beam (support spacing), h1 and h2 represent the thickness of the connecting plate and the height of the concrete beam, respectively, and b1 and b2 represent the width of the connecting plate and the width of the concrete beam, respectively. Detailed Implementation

[0013] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. Example 1

[0014] The RHHR support arrangement is a symmetrical structure. To simplify the calculation and analysis, the structure can be truncated along the axis of symmetry, and the "half-structure" on one side can be analyzed.

[0015] The deformation and stress diagram of the continuous bridge deck structure under the RHHR support arrangement is shown below. Figure 3 As shown. This invention proposes a macroscopic mechanical model for the calculation and analysis of a continuous bridge deck structure under the RHHR support arrangement, comprising: assuming a symmetrical load arrangement under the RHHR support arrangement, here a "semi-structure" analysis is adopted, the unbonded connecting plate is broken in the middle, and a roller bearing is added in the middle of the unbonded connecting plate. This roller bearing is used to constrain the bending moment and longitudinal bridge degree of freedom, and release the vertical degree of freedom, as shown. Figure 4 As shown. Example 2

[0016] A method for deriving the governing equations of the macroscopic mechanical model described in Embodiment 1 of the present invention, the method being based on the displacement method, comprising the following steps: First, under the action of external load, the beam end rotated. The elongation of the reinforcing bars in the unbonded slab, , can be represented as: (1) In the formula, It is the distance between the neutral axis of the composite section and the neutral axis of the connecting plate; It is the distance between the neutral axis of the composite section and the central axis of the concrete beam section; It is the height of the neutral axis of the concrete beam; This refers to the angle of rotation of the concrete beam at the support position.

[0017] At this moment, the tension in the connecting plate It can be calculated using the following formula: (2) In the formula, , and The geometric dimensional parameters for the connecting plate area are as follows: For the transition interface and support spacing; The distance between the support and the end of the concrete beam; The distance from the end of the concrete beam to the center of the connecting plate; For example Figure 4 As indicated by the annotations in the document, and These are the elastic modulus and cross-sectional area of ​​the reinforcing bars in the connecting plate, respectively.

[0018] like Figure 5 As shown, a composite beam segment refers to a beam segment outside the connecting plate area that shares the load with the concrete bridge deck and concrete beams. For example... Figure 6 As shown, the bending moment at the interface between the connecting plate and the composite beam segment and the bending moment borne by the virtual rigid arm at the contact point. It can be represented as: (3) (4) In the formula, It is the bending stiffness of the connecting plate; and These refer to the corners of the transition interface and the contact point, respectively. and These represent the vertical displacements of the transition interface and the contact point, respectively.

[0019] It should be noted that the transition interface refers to the transition interface between the connecting plate and the composite beam segment; the contact point refers to the point of contact between the connecting plate and the concrete beam segment below it when the connecting plate undergoes bending deformation under external load.

[0020] Shear force at the transition interface Contact force at the contact point It can be represented as: (5) (6) like Figure 7 As shown, the bending moment at the transition section The bending moment borne by the virtual rigid arm above the hinged support (a virtual rigid arm is used to constrain the rotational degree of freedom at a point in the structure) It can be represented as: (7) (8) In the formula, It refers to the bending stiffness of a concrete beam.

[0021] Shear force at the transition interface Contact force at the contact point It can be represented as: (9) (10) like Figure 8 As shown, the bending moment at the transition interface and shear force It can be represented as: (11) (12) Furthermore, the moment equilibrium condition at the virtual rigid arm is: (13) (14) The force equilibrium condition at the point of contact is: (15) By solving equations (11)-(15) simultaneously and performing differentiation, the governing equations of the macroscopic mechanical model can be obtained: (16) In the formula, These are the displacement increment vector and the force increment vector, respectively. This is the tangent stiffness matrix of the macroscopic mechanical model proposed in this invention. , , , For a matrix, calculate according to the following formulas: (17) (18) (19) (20). Example 3

[0022] For bridge deck continuous structures with RHHR support arrangement, such as Figure 9As shown, this invention can combine macroscopic mechanical models and planar beam elements. Using macroscopic mechanical models can effectively improve computational efficiency while ensuring computational accuracy. Specifically, the macroscopic mechanical model is used to simulate the structural stress within the continuous section (connecting plate) of the bridge deck, while the planar beam elements are used to simulate the structural stress outside the continuous section (connecting plate) of the bridge deck. The concrete and steel reinforcement materials in the planar beam elements can adopt nonlinear constitutive models, which can be used to consider the influence of material nonlinearity on the continuous structure of the bridge deck in the calculation and analysis.

[0023] The continuous bridge deck structure in this embodiment is as follows: Figure 10 As shown in Table 1, the parameters of the concrete material are shown in Table 1, and the values ​​of each parameter in the continuous bridge deck structure are shown in Table 2. The change in mid-span deflection of the concrete beam with the loading of vertical force P is shown in Table 2. Figure 11 As shown, the mid-span deflection calculated using a macroscopic mechanical model and planar beam elements is basically consistent with the experimental results, with a maximum error of 12%, indicating that the calculation results have been verified by the experimental results.

[0024] Table 1 Material design parameters for concrete bridge decks and concrete beams Table 2 Parameter Values Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A calculation and analysis method for continuous bridge deck structures applicable to RHHR support arrangement, characterized in that, This includes establishing a macroscopic mechanical model: under the RHHR support arrangement, assuming a symmetrical load arrangement, taking a half-structure analysis, the unbonded connecting plate is broken in the middle, and a roller support is added in the middle of the unbonded connecting plate to constrain the bending moment and longitudinal bridge degree of freedom, and release the vertical degree of freedom. Here, R represents a sliding support and H represents a hinged support.

2. The calculation and analysis method for bridge deck continuous structures applicable to RHHR support arrangement as described in claim 1, characterized in that, The governing equations of the macroscopic mechanical model are: (16)， In the formula, These are the displacement increment vector and the force increment vector, respectively. This is the tangent stiffness matrix of the macroscopic mechanical model.

3. The calculation and analysis method for bridge deck continuous structures applicable to RHHR support arrangement as described in claim 2, characterized in that, The derivation process of the governing equations for the macroscopic mechanical model includes: Under the action of external load, the beam end rotated. The elongation of the reinforcing bars in the unbonded joint plate Represented as: (1)， In the formula, It is the distance between the neutral axis of the composite section and the neutral axis of the connecting plate; It is the distance between the neutral axis of the composite section and the central axis of the concrete beam section; It is the height of the neutral axis of the concrete beam; This refers to the rotation angle of the concrete beam at the support position; At this moment, the tension in the connecting plate Calculate according to the following formula: (2)， In the formula, For the transition interface and support spacing; The distance between the support and the end of the concrete beam; The distance from the end of the concrete beam to the center of the connecting plate; and These are the elastic modulus and cross-sectional area of ​​the reinforcing bars in the connecting plate, respectively. Bending moment at the interface between the connecting plate and the composite beam segment and the bending moment borne by the virtual rigid arm at the contact point. Represented as: (3)， (4)， In the formula, It is the bending stiffness of the connecting plate; and These refer to the corners of the transition interface and the contact point, respectively. and These represent the vertical displacements of the transition interface and the contact point, respectively. Shear force at the transition interface Contact force at the contact point Represented as: (5)， (6)， Bending moment at transition section The bending moment borne by the virtual rigid arm above the hinge support Represented as: (7)， (8)， In the formula, It refers to the flexural stiffness of a concrete beam; Shear force at the transition interface Contact force at the contact point Represented as: (9)， (10)， Bending moment at the transition interface and shear force Represented as: (11)， (12)， Furthermore, the moment equilibrium condition at the virtual rigid arm is: (13)， (14)， The force equilibrium condition at the point of contact is: (15)， Solve the equations (11)-(15) simultaneously and perform differentiation to obtain the governing equation (16) of the macroscopic mechanical model.

4. The calculation and analysis method for bridge deck continuous structures under the support arrangement applicable to RHHR as described in claim 2 or 3, characterized in that, The , , , Calculate according to the following formulas: (17)， (18)， (19)， (20)。

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