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

Abstract

The application discloses a bridge deck continuous structure calculation analysis method suitable for a support arrangement form of HRRH, relates to the field of bridge engineering, and comprises the following steps: a macro mechanics model is established; in the support arrangement form of HRRH, symmetric load arrangement is assumed, half-structure analysis is carried out, unbonded connecting plates are disconnected from the middle, vertical roller shaft supports are additionally arranged in the middle of the unbonded connecting plates and are used for constraining axial and rotating degrees of freedom and releasing the vertical sliding degree of freedom, wherein R represents a sliding support, and H represents a hinged support. The method is suitable for the calculation analysis of the bridge deck continuous structure, can consider the influence of different support arrangement forms and is used for guiding the design of the bridge.

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 different bearing arrangements applicable to HRRH (High-Rise Reverse Harbor Bridge). This method 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, research has demonstrated that different support arrangements significantly impact the stress on continuous bridge deck structures. Existing computational analysis methods are mainly divided 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

[0004] 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 HRRH support arrangement, applicable to the calculation and analysis of continuous bridge deck structures, taking into account the influence of different support arrangement forms, and used to guide the design of this type of bridge.

[0005] 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 HRRH bearing arrangement includes establishing a macroscopic mechanical model: under the HRRH bearing arrangement, assuming symmetrical load arrangement, half-structure analysis is performed, the unbonded connecting plate is broken in the middle, and a vertical roller bearing is added in the middle of the connecting plate. The vertical roller bearing is used to constrain axial and rotational degrees of freedom and release vertical sliding degrees of freedom, where R represents a sliding bearing and H represents a hinge bearing.

[0006] Furthermore, the governing equations of the macroscopic mechanical model are: (15), In the formula, This is the tangent stiffness matrix of the macroscopic mechanical model.

[0007] Furthermore, the derivation process of the governing equations of the macroscopic mechanical model includes: Under external load, the elongation of the reinforcing bars in the unbonded slab is: Then the tension of the connecting plate for: (1), In the formula, This refers to the elastic modulus of the reinforcing steel. This represents the cross-sectional area of ​​the reinforcing steel. , and Here are the geometric dimensional parameters of the connecting plate region, where, 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; The distance between the neutral axis of the connecting plate and the neutral axis of the composite section; The distance between the neutral axis of the concrete beam and the neutral axis of the composite section; 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.

[0008] 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: (2), (3), 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: (4), (5), Bending moment at transition section The bending moment borne by the virtual rigid arm above the hinge support Represented as: (6), (7), 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: (8), (9), Bending moment at the transition interface and shear force Represented as: (10), (11), The moment equilibrium condition at the virtual rigid arm is: (12), (13), The force equilibrium condition at the point of contact is: (14), Solve the equations (10)-(14) simultaneously and perform differentiation to obtain the governing equation (15) of the macroscopic mechanical model.

[0009] Furthermore, the aforementioned , , , Calculate according to the following formulas: (16), (17), (18), (19).

[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 continuous bridge deck structure can be obtained by solving the governing equations, and it can be used in conjunction with planar beam elements (as shown in the appendix). Figure 4 As shown in the figure, it has higher computational efficiency compared to the spatial finite element model (three-dimensional solid element); (c) The macroscopic mechanical model of this invention can be used in conjunction with planar beam elements (as shown in the appendix). Figure 4 As shown in the figure, in a planar beam element, the influence of material nonlinearity can be considered, which can improve the calculation accuracy compared to a simplified analysis model. Attached Figure Description

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

[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 HRRH support arrangement is a symmetrical structure. To simplify the calculation and analysis of this symmetrical structure, it can be truncated from 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 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 HRRH support arrangement, comprising: assuming a symmetrical load arrangement under the HRRH support arrangement (here, a "semi-structure" analysis is adopted), the unbonded connecting plate is broken in the middle, and a vertical roller bearing is added in the middle of the unbonded connecting plate. This roller bearing is used to constrain the axial and rotational degrees of freedom and release the vertical sliding 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 external load, the elongation of the reinforcing bars in the unbonded slab is... Then the tension of the connecting plate for: (1) In the formula, This refers to the elastic modulus of the reinforcing steel. This represents the cross-sectional area of ​​the reinforcing steel. , and Here are the geometric dimensional parameters of the connecting plate region, where, 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; The distance between the neutral axis of the connecting plate and the neutral axis of the composite section; The distance between the neutral axis of the concrete beam and the neutral axis of the composite section; 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] like Figure 5As shown, a composite beam segment refers to a beam segment outside the range of the connecting plate that is jointly stressed by a concrete bridge deck and a concrete beam.

[0018] like 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: (2) (3) 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: (4) (5) like Figure 7 As shown, the bending moment at the transition section The bending moment borne by the virtual rigid arm above the hinge support It can be represented as: (6) (7) 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: (8) (9) like Figure 8 As shown, the bending moment at the transition interface and shear force It can be represented as: (10) (11) Furthermore, the moment equilibrium condition at the virtual rigid arm is: (12) (13) The force equilibrium condition at the point of contact is: (14) By solving equations (10)-(14) simultaneously and performing differentiation, the governing equations of the macroscopic mechanical model can be obtained as follows: (15) In the formula, These are the displacement increment vector and the force increment vector, respectively. This refers to the tangent stiffness matrix of the macroscopic mechanical model proposed in this invention patent. , , , For a matrix, calculate according to the following formulas: (16) (17) (18) (19). Example 3

[0022] The macroscopic mechanical model proposed in this invention has governing equations as shown in Example 2, which are derived from the stiffness matrix. Expression displacement increment matrix Internal Force Increment Array It possesses the same theoretical framework as the finite element method, and therefore can be used in conjunction with planar beam elements. For continuous bridge deck structures with HRRH support arrangements, such as... Figure 9 As shown, the macroscopic mechanical model and planar beam element proposed in this invention are combined and used, as follows: Figure 10 As shown, planar beam elements are used to simulate the structural stress outside the continuous bridge deck section (connecting plate). By setting nonlinear material properties for concrete and steel reinforcement in the planar beam elements, the influence of material nonlinearity on the continuous bridge deck structure can be considered in the calculation and analysis. Using a macroscopic mechanical model effectively improves computational efficiency while ensuring computational accuracy.

[0023] The schematic diagram of the continuous bridge deck structure in this example is shown below. 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 11As 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 8%, 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 HRRH support arrangements, characterized in that, This includes establishing a macroscopic mechanical model: under the HRRH support arrangement, assuming a symmetrical load arrangement, taking a half-structure analysis, the unbonded connecting plate is broken in the middle, and a vertical roller support is added in the middle of the unbonded connecting plate to constrain the axial and rotational degrees of freedom and release the vertical sliding degree of freedom, where R represents the sliding support and H represents the hinge support.

2. The calculation and analysis method for bridge deck continuous structures under the support arrangement applicable to HRRH as described in claim 1, characterized in that, The governing equations of the macroscopic mechanical model are: (15)， 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 under the support arrangement applicable to HRRH as described in claim 1 or 2, characterized in that, The derivation process of the governing equations for the macroscopic mechanical model includes: Under external load, the elongation of the reinforcing bars in the unbonded slab is: Then the tension of the connecting plate for: (1)， In the formula, This refers to the elastic modulus of the reinforcing steel. This represents the cross-sectional area of ​​the reinforcing steel. 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; The distance between the neutral axis of the connecting plate and the neutral axis of the composite section; The distance between the neutral axis of the concrete beam and the neutral axis of the composite section; The height of the neutral axis of the concrete beam; This refers to the rotation angle of the concrete beam at the support position; 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: (2)， (3)， 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: (4)， (5)， Bending moment at transition section The bending moment borne by the virtual rigid arm above the hinge support Represented as: (6)， (7)， 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: (8)， (9)， Bending moment at the transition interface and shear force Represented as: (10)， (11)， The moment equilibrium condition at the virtual rigid arm is: (12)， (13)， The force equilibrium condition at the point of contact is: (14)， Solve the equations (10)-(14) simultaneously and perform differentiation to obtain the governing equation (15) of the macroscopic mechanical model.

4. The calculation and analysis method for bridge deck continuous structures under the support arrangement applicable to HRRH as described in claim 3, characterized in that, The , , , Calculate according to the following formulas: (16)， (17)， (18)， (19)。

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