Shaft bending shear coupling analysis method of reinforced concrete rectangular hollow pier

Abstract

The invention provides an axial bending-shearing coupling analysis method for a rectangular hollow reinforced concrete pier, and relates to the technical field of constructional engineering.The method comprises the steps that based on a reinforced concrete elastic-plastic damage constitutive, plastic strain evolution data are obtained through calculation; performing rectangular hollow pier discretization on the reinforced concrete elastic-plastic damage constitutive structure to obtain discretized data; performing shaft bending shear coupling analysis on the rectangular hollow pier to obtain an initial coupling analysis result; the initial coupling analysis result is verified, when the initial coupling analysis result meets verification conditions, a final coupling analysis result is obtained, and shaft bending shear coupling analysis of the reinforced concrete rectangular hollow pier is completed. The method solves the problem that the nonlinear behavior of the reinforced concrete rectangular hollow pier is difficult to accurately and efficiently predict.

Description

Technical Field

[0001] This specification relates to the technical field of construction engineering, and particularly to a method for analyzing the axial-flexural-shear coupling of reinforced concrete rectangular hollow piers. Background Art

[0002] Reinforced concrete rectangular hollow piers are widely used in dangerous mountainous areas. Due to the hollow cross-section, their shear resistance is weakened, and they are prone to flexural-shear damage under strong earthquake actions, with significant flexural-shear effects. Accurately predicting the nonlinear behavior of reinforced concrete rectangular hollow piers is crucial for seismic design and directly affects the seismic safety of bridges in dangerous mountainous areas.

[0003] However, the commonly used fiber beam element model in seismic analysis can only simulate axial-flexural behavior. Ignoring the flexural-shear coupling effect will underestimate the seismic displacement response of reinforced concrete rectangular hollow piers, bringing potential risks to seismic design. Among the existing analysis theories and methods considering the flexural-shear effect, the shear spring model (Xu et al., 2011) does not reflect the physical mechanism of flexural-shear, and its accuracy depends on specific data calibration; the calculation results of the beam-truss model (Lu et al., 2016) are greatly affected by component disassembly skills and mechanical parameters; the multi-vertical plate model SFI-MVLEM considering flexural-shear coupling (Kolozvari et al., 2021) is difficult to consider the strength degradation caused by steel bar fracture; the Timoshenko fiber beam model based on multi-axial material constitutive (Ceresa et al., 2009) has poor numerical convergence and low calculation efficiency. Summary of the Invention

[0004] Aiming at the above deficiencies in the prior art, a method for analyzing the axial-flexural-shear coupling of reinforced concrete rectangular hollow piers provided by the present invention solves the problem of difficult to accurately and efficiently predict the nonlinear behavior of reinforced concrete rectangular hollow piers.

[0005] To achieve the above invention object, the technical solution adopted by the present invention is: a method for analyzing the axial-flexural-shear coupling of reinforced concrete rectangular hollow piers, including:

[0006] S1: Based on the elastoplastic damage constitutive of reinforced concrete, through calculation, obtain the plastic strain evolution data;

[0007] S2: Based on the plastic strain evolution data, discretize the elastoplastic damage constitutive of reinforced concrete for the rectangular hollow pier to obtain discretized data;

[0008] S3: Based on the discretized data, conduct axial-flexural-shear coupling analysis on the rectangular hollow pier to obtain the initial coupling analysis result;

[0009] S4: Verify the initial coupling analysis result. When the initial coupling analysis result meets the verification conditions, obtain the final coupling analysis result to complete the axial-bending-shear coupling analysis of the reinforced concrete rectangular hollow pier.

[0010] Further, the S1 includes:

[0011] Based on the elastic-plastic damage constitutive model of the reinforced concrete, obtain the total strain tensor through measurement;

[0012] Use the strain equivalence principle to calculate the total strain tensor to obtain the effective stress tensor;

[0013] Obtain the total Helmholtz free energy of the damaged material by analyzing the degradation of the Helmholtz free energy under the action of the effective stress tensor;

[0014] Based on the total Helmholtz free energy of the damaged material, obtain the plastic strain evolution data through calculation. Further, the expression of the total strain tensor is:

[0015] ε = ε e + ε p ;

[0016] The expression of the effective stress tensor is:

[0017]

[0018] where ε represents the total strain tensor, ε e represents the elastic strain tensor, ε p represents the plastic strain tensor, represents the effective stress tensor, E 0 represents the fourth-order elastic stiffness matrix of the isotropic material, represents the tensile component of the effective stress tensor, represents the Iverson bracket, represents the i-th effective principal stress, p i represents the unit vector in the corresponding principal direction, represents the vector product, represents the compressive component of the effective stress tensor.

[0019] Further, the expression of the total Helmholtz free energy of the damaged material is:

[0020]

[0021]

[0022] where Ψ represents the total Helmholtz free energy of the damaged material, ε represents the total strain tensor, ε p represents the plastic strain tensor, d +denotes the tensile damage variable, d - denotes the compressive damage variable, denotes the first initial elastic free energy of the elastic damage material, denotes the second initial elastic free energy of the elastic damage material, denotes the tensile component of the effective stress tensor, denotes the compressive component of the effective stress tensor, E 0 denotes the fourth-order elastic stiffness matrix of the isotropic material, denotes the effective stress tensor.

[0023] Furthermore, the expressions for the tensile damage variable and the compressive damage variable are respectively:

[0024]

[0025] where, d + denotes the tensile damage variable, Y0 + denotes the initial tensile damage energy release rate, Y + denotes the tensile damage energy release rate, A + denotes the parameter closely related to the descending section of the tensile stress-strain constitutive relationship, d - denotes the compressive damage variable, denotes the initial compressive damage energy release rate, Y - denotes the compressive damage energy release rate, A - denotes the parameter describing the stress softening effect of concrete material before the uniaxial compressive peak stress, B - denotes the parameter describing the softening effect occurring after the peak stress point, denotes the tensile component of the effective stress tensor, E 0 denotes the fourth-order elastic stiffness matrix of the isotropic material, K denotes the material parameter considering the biaxial compression effect, denotes the octahedral effective normal stress, denotes the octahedral effective shear stress.

[0026] Furthermore, the expression for the plastic strain evolution data is:

[0027]

[0028]

[0029] where, denotes the plastic strain evolution data, β str denotes the material parameter introduced to control the rate and strength of plastic deformation, E0 denotes the fourth-order elastic stiffness matrix of the isotropic material, σ denotes the Cauchy stress, Ψ denotes the total Helmholtz free energy of the damaged material, ε denotes the total strain tensor, d +denotes the tensile damage variable, denotes the first initial elastic free energy of the elastic damage material, ε e denotes the elastic strain tensor, d - denotes the compressive damage variable, denotes the second initial elastic free energy of the elastic damage material, denotes the tensile component of the effective stress tensor, denotes the compressive component of the effective stress tensor, I denotes the fourth-order identity tensor, D denotes the fourth-order damage tensor, denotes the effective stress tensor, E(d) denotes the unloading stiffness of the material.

[0030] Furthermore, the S2 includes:

[0031] Based on the plastic strain evolution data, divide the rectangular hollow pier of the reinforced concrete elasto-plastic damage constitutive into an axial-bending region and an axial-shear region;

[0032] Use fiber beam elements to simulate the mechanical behavior of the axial-bending region to obtain discretized data of the axial-bending region;

[0033] Use membrane elements of the elasto-plastic damage constitutive to simulate the mechanical behavior of the axial-shear region to obtain discretized data of the axial-shear region;

[0034] By maintaining degrees of freedom, coordinate the forces and deformations of the coincident nodes at the boundaries of the axial-bending region and the axial-shear region to obtain discretized data of the boundary region;

[0035] Integrate the discretized data of the axial-bending region, the discretized data of the axial-shear region, and the discretized data of the boundary region to obtain discretized data.

[0036] The beneficial effects of the present invention are: a method for analyzing the axial-bending-shear coupling of a reinforced concrete rectangular hollow pier. 1) It can consider the compressive softening effect, strength degradation, and unloading stiffness degradation caused by shear damage of concrete within the unified theoretical framework of the elasto-plastic damage constitutive, with stronger theoreticality; 2) Numerically discretize the rectangular hollow pier using membrane-beam-truss elements, which not only conforms to the bending-shear force mechanism but also improves the modeling and calculation efficiency; 3) This method can completely reproduce the nonlinear hysteretic characteristics of rectangular hollow piers with different shear-span ratios and different failure modes, and has very good accuracy and convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] This specification will be further described in the form of exemplary embodiments, and these exemplary embodiments will be described in detail through the drawings. These embodiments are not restrictive, and in these embodiments, the same numbers represent the same structures, where:

[0038] Figure 1An exemplary flowchart of an axial-bending-shear coupling analysis method for a reinforced concrete rectangular hollow pier as shown in some embodiments of this specification;

[0039] Figure 2 An exemplary schematic diagram of a uniaxial concrete constitutive model and a uniaxial steel bar constitutive model as shown in some embodiments of this specification. Detailed implementation manners

[0040] The following describes the detailed implementation manners of the present invention to facilitate those skilled in the art to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed implementation manners. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0041] Embodiment

[0042] Figure 1 An exemplary flowchart of an axial-bending-shear coupling analysis method for a reinforced concrete rectangular hollow pier as shown in some embodiments of this specification. As Figure 1 shown, the process includes the following steps. In some embodiments, the process can be executed by a processor.

[0043] S1: Based on the elastoplastic damage constitutive model of reinforced concrete, through calculation, obtain the plastic strain evolution data.

[0044] The elastoplastic damage constitutive model of reinforced concrete is a physical model used to calculate the elastoplastic damage relationship of reinforced concrete.

[0045] The plastic strain evolution data is data reflecting the change of the plastic deformation of the elastoplastic damage constitutive model of reinforced concrete over time.

[0046] In some embodiments, the processor can implement S1 based on the following steps: Based on the elastoplastic damage constitutive model of reinforced concrete, through measurement, obtain the total strain tensor; using the strain equivalence principle, calculate the total strain tensor to obtain the effective stress tensor; by analyzing the degradation of the Helmholtz free energy under the action of the effective stress tensor, obtain the total Helmholtz free energy of the damaged material; based on the total Helmholtz free energy of the damaged material, through calculation, obtain the plastic strain evolution data.

[0047] The total strain tensor is the sum of all strain tensors of the elastoplastic damage constitutive model of reinforced concrete.

[0048] In some embodiments, the expression of the total strain tensor can be:

[0049] ε = ε e + ε p ;

[0050] Among them, ε represents the total strain tensor, ε e represents the elastic strain tensor, ε p represents the plastic strain tensor.

[0051] The effective stress tensor is the stress tensor related to the material strain.

[0052] In some embodiments, the expression of the effective stress tensor can be:

[0053]

[0054] Among them, represents the effective stress tensor, E 0 represents the fourth-order elastic stiffness matrix of the isotropic material, represents the tensile component of the effective stress tensor, represents the Iverson bracket, represents the i-th effective principal stress, p i represents the unit vector in the corresponding principal direction, represents the vector product, represents the compressive component of the effective stress tensor.

[0055] The total Helmholtz free energy of the damaged material is a thermodynamic state function reflecting the situation of the damaged material.

[0056] In some embodiments, the expression of the total Helmholtz free energy of the damaged material can be:

[0057]

[0058] Among them, Ψ represents the total Helmholtz free energy of the damaged material, ε represents the total strain tensor, ε p represents the plastic strain tensor, d + represents the tensile damage variable, d - represents the compressive damage variable, represents the first initial elastic free energy of the elastically damaged material, represents the second initial elastic free energy of the elastically damaged material, represents the tensile component of the effective stress tensor, represents the compressive component of the effective stress tensor, E 0 represents the fourth-order elastic stiffness matrix of the isotropic material, represents the effective stress tensor.

[0059] In some embodiments, the expressions of the tensile damage variable and the compressive damage variable can be respectively:

[0060]

[0061] Among them, d + represents the tensile damage variable, represents the initial tensile damage energy release rate, Y + represents the tensile damage energy release rate, A + represents the parameter closely related to the descending section of the tensile stress-strain constitutive relationship, d - represents the compressive damage variable, represents the initial compressive damage energy release rate, Y - represents the compressive damage energy release rate, A - represents the parameter describing the stress softening effect of concrete materials before the uniaxial compressive peak stress, B - represents the parameter describing the softening effect occurring after the peak stress point, represents the tensile component of the effective stress tensor, E 0 represents the fourth-order elastic stiffness matrix of an isotropic material, K represents the material parameter considering the biaxial compression effect, represents the octahedral effective normal stress, represents the octahedral effective shear stress.

[0062] In some embodiments, the expression of the plastic strain evolution data can be:

[0063]

[0064] Among them, represents the plastic strain evolution data, β str represents the material parameter introduced to control the rate and strength of plastic deformation, E0 represents the fourth-order elastic stiffness matrix of an isotropic material, σ represents the Cauchy stress, Ψ represents the total Helmholtz free energy of the damaged material, ε represents the total strain tensor, d + represents the tensile damage variable, represents the first initial elastic free energy of the elastic damaged material, ε e represents the elastic strain tensor, d - represents the compressive damage variable, represents the second initial elastic free energy of the elastic damaged material, represents the tensile component of the effective stress tensor, represents the pressure component of the effective stress tensor, I represents the fourth-order unit tensor, D represents the fourth-order damage tensor, represents the effective stress tensor, E(d) represents the unloading stiffness of the material.

[0065] In this way, the coupling of damage evolution and plastic evolution can be achieved. At this time, the coupling between damage and plasticity is simplified, and no additional iteration is required during the determination of the material state, thus taking into account both the accuracy and efficiency of the numerical model for the nonlinear seismic analysis of large-scale structures. In short, the elasto-plastic damage constitutive model can simultaneously consider the compressive softening effect, strength degradation, and stiffness degradation during loading and unloading caused by shear damage of concrete, with stronger theoretical basis.

[0066] S2: Based on the plastic strain evolution data, discretize the reinforced concrete elasto-plastic damage constitutive model for the rectangular hollow pier to obtain discretized data.

[0067] The discretized data are the data after discretization of each node of the rectangular hollow pier. For example, the discretized data may include discretized data of the axial-bending region, axial-shear region, and boundary region.

[0068] In some embodiments, the processor can implement S2 based on the following steps: Based on the plastic strain evolution data, divide the rectangular hollow pier of the reinforced concrete elasto-plastic damage constitutive model into an axial-bending region and an axial-shear region; use fiber beam elements to simulate the mechanical behavior of the axial-bending region to obtain discretized data of the axial-bending region; use membrane elements of the elasto-plastic damage constitutive model to simulate the mechanical behavior of the axial-shear region to obtain discretized data of the axial-shear region; through the way of maintaining degrees of freedom, coordinate the forces and deformations of the coincident nodes at the boundary between the axial-bending region and the axial-shear region to obtain discretized data of the boundary region; combine the discretized data of the axial-bending region, the discretized data of the axial-shear region, and the discretized data of the boundary region to obtain the discretized data.

[0069] The axial-bending region is the short-side region of the rectangular hollow pier.

[0070] The axial-shear region is the long-side region of the rectangular hollow pier.

[0071] In some embodiments, the processor can merge the axial-shear regions into one region. At this time, the three-dimensional hollow section can be equivalent to a two-dimensional hollow section.

[0072] The discretized data of the axial-bending region are the data after discretization of the nodes in the axial-bending region.

[0073] In some embodiments, as Figure 2 shown, the processor can use fiber beam elements composed of uniaxial concrete constitutive model and uniaxial steel constitutive model to simulate the mechanical behavior of the axial-bending region to obtain discretized data of the axial-bending region; among them, the fiber cross-section includes confined concrete behavior, unconfined concrete fibers, and steel fibers.

[0074] The discretized data of the axial-shear region are the data after discretization of the nodes in the axial-shear region.

[0075] In some embodiments, the processor may simulate the steel bars in the axial-shear region as truss elements based on the uniaxial steel bar constitutive model. The membrane elements and truss elements share the same nodes. By using the membrane elements with elastoplastic damage constitutive model, the mechanical behavior of the axial-shear region is simulated to obtain the discretized data of the axial-shear region.

[0076] The discretized data of the boundary region is the data obtained after discretizing the nodes at the boundary between the axial-bending region and the axial-shear region.

[0077] In some embodiments, the processor may make the force and deformation coordinated by keeping the degrees of freedom the same for the coincident nodes at the boundary between the axial-bending region and the axial-shear region. The nodes at the top of the pier are connected by rigid beam elements, and the nodes at the bottom of the pier are directly fixed.

[0078] In some embodiments, the processor may use the discretized data to construct a physical model for the axial-bending-shear coupling analysis of the rectangular hollow pier. In this way, at the material level, the physical mechanism of bending-shear damage is considered through the two-dimensional elastoplastic damage constitutive model; at the element level, the rectangular hollow pier is numerically discretized by membrane-beam-truss hybrid elements to reflect its bending-shear mechanical behavior.

[0079] S3: Based on the discretized data, perform axial-bending-shear coupling analysis on the rectangular hollow pier to obtain the initial coupling analysis result.

[0080] The initial coupling analysis result is the output result of performing axial-bending-shear coupling analysis on the rectangular hollow pier using software. For example, the initial coupling analysis result may include the initial coupling analysis result of the axial-shear region, the initial coupling analysis result of the axial-bending region, and other physical models of the specimen.

[0081] In some embodiments, the processor may use four-node membrane (plane stress) elements to simulate the concrete in the axial-shear region and use PlasticDamageConcretePlaneStress to simulate the two-dimensional elastoplastic damage constitutive model; the membrane elements need to be divided according to the size and calculation efficiency of the axial-shear region of the component; the steel bars in the axial-shear region are simulated by truss elements (Truss Element); and, the truss elements in the axial-shear region share the same nodes with the four-node membrane elements. The cross-sectional area of the truss element is obtained after conversion according to the principle of equivalent reinforcement ratio. The uniaxial material constitutive model of the truss element can adopt the ReinforcingSteel model to simulate and obtain the initial coupling analysis result of the axial-shear region.

[0082] In some embodiments, the processor may use fiber beam elements to simulate the reinforced concrete in the shaft bending region. The Concrete01 model can be selected as the uniaxial material constitutive model of concrete fibers. The calculation parameters of the core concrete and cover concrete fibers can be obtained according to the measured material strength and the confinement and unconfined concrete stress-strain models proposed by Mander. The ReinforcingSteel model can be used as the uniaxial material constitutive model of steel fibers to obtain the initial coupling analysis results in the shaft bending region.

[0083] The fiber beam elements include the force-based fiber element "forceBeamColumn" (also known as nonlinearBeamColumn) and the displacement-based fiber element "dispBeamColumn". The cross-section of the fiber element is generally divided into three types: core concrete fibers, cover concrete fibers, and steel fibers.

[0084] In some embodiments, the processor may implement the numerical analysis of the shaft-bending and shear model of the rectangular hollow pier based on the following process: The coupling in space between the shaft shear region and the shaft bending region is considered by synchronizing the nodal degrees of freedom of the membrane elements and the fiber elements, which is implemented by means of the "equalDOF" command in the OpenSees program. The nodes of the fiber elements in the shaft bending region and the nodes of the membrane elements at the junction with the shaft shear region generally have the same coordinates. The axial force of the reinforced concrete member is directly distributed evenly among the top nodes, and these nodes are connected by rigid beam elements. Further, a horizontal displacement time history can be applied at the top of the reinforced concrete member for pseudo-static loading, or the seismic motion time history conditions can be set after adding lumped masses (Mass) to each node for dynamic loading, so as to study the bending-shear coupling behavior of the rectangular hollow pier.

[0085] S4: Verify the initial coupling analysis results. When the initial coupling analysis results meet the verification conditions, obtain the final coupling analysis results, and complete the shaft-bending and shear coupling analysis of the reinforced concrete rectangular hollow pier.

[0086] The final coupling analysis results are the initial coupling analysis results that can accurately reproduce the hysteretic characteristics of the specimen.

[0087] In some embodiments, the processor may perform finite element modeling and calculation on the initial coupling analysis results, predict the initial stiffness, yield plateau, peak strength, and residual displacement of the hollow pier specimen, and use the initial coupling analysis results that can accurately reproduce the hysteretic characteristics such as strength degradation, stiffness degradation, pinching effect, and hysteretic energy dissipation of the specimen as the final coupling analysis results.

[0088] In some embodiments of this specification, a method for the coupled axial-flexural-shear analysis of reinforced concrete rectangular hollow piers is proposed. 1) It can consider the compressive softening effect, strength degradation, and stiffness degradation during loading and unloading caused by shear damage of concrete within the unified theoretical framework of elasto-plastic damage constitutive models, with stronger theoreticality; 2) The rectangular hollow pier is numerically discretized using membrane-beam-truss elements, which not only conforms to the flexural-shear force mechanism but also improves the modeling and calculation efficiency; 3) This method can completely reproduce the nonlinear hysteretic characteristics of rectangular hollow piers with different shear-span ratios and different failure modes, and has very good accuracy and convergence.

Claims

1. A method for analyzing the axial-bending-shear coupling of a reinforced concrete rectangular hollow pier, characterized in that, Including: S1: Based on the elastoplastic damage constitutive model of reinforced concrete, through calculation, obtain the plastic strain evolution data; S2: Based on the plastic strain evolution data, discretize the elastoplastic damage constitutive model of reinforced concrete for the rectangular hollow pier to obtain discretized data; S3: Based on the discretized data, conduct an axial-bending-shear coupling analysis of the rectangular hollow pier to obtain the initial coupling analysis result; S4: Verify the initial coupling analysis result. When the initial coupling analysis result meets the verification conditions, obtain the final coupling analysis result, and complete the axial-bending-shear coupling analysis of the reinforced concrete rectangular hollow pier.

2. The method for analyzing the axial-bending-shear coupling of a reinforced concrete rectangular hollow pier according to claim 1, wherein The S1 includes: Based on the elastoplastic damage constitutive model of reinforced concrete, through measurement, obtain the total strain tensor; Using the strain equivalence principle, calculate the total strain tensor to obtain the effective stress tensor; By analyzing the degradation of the Helmholtz free energy under the action of the effective stress tensor, obtain the total Helmholtz free energy of the damaged material; Based on the total Helmholtz free energy of the damaged material, through calculation, obtain the plastic strain evolution data.

3. The method for analyzing the axial-bending-shear coupling of the reinforced concrete rectangular hollow pier according to claim 2, characterized in that The expression of the total strain tensor is: ε = ε e + ε p ; The expression of the effective stress tensor is: where ε represents the total strain tensor, ε e represents the elastic strain tensor, ε p represents the plastic strain tensor, represents the effective stress tensor, E 0 represents the fourth-order elastic stiffness matrix of the isotropic material, represents the tensile component of the effective stress tensor, represents the Iverson bracket, represents the i-th effective principal stress, p i represents the unit vector in the corresponding principal direction, represents the vector product, represents the compressive component of the effective stress tensor.

4. The method for analyzing the axial-bending-shear coupling of a reinforced concrete rectangular hollow pier according to claim 2, characterized in that, The expression of the total Helmholtz free energy of the damaged material is: Among them, Ψ represents the total Helmholtz free energy of the damaged material, ε represents the total strain tensor, and ε p represents the plastic strain tensor, d + represents the tensile damage variable, d - represents the compressive damage variable, represents the first initial elastic free energy of the elastically damaged material, represents the second initial elastic free energy of the elastically damaged material, represents the tensile component of the effective stress tensor, represents the compressive component of the effective stress tensor, E 0 represents the fourth-order elastic stiffness matrix of the isotropic material, represents the effective stress tensor.

5. The method for analyzing the axial-flexural-shear coupling of a reinforced concrete rectangular hollow pier according to claim 4, wherein The expressions of the tensile damage variable and the compressive damage variable are respectively: Among them, d + represents the tensile damage variable, represents the initial tensile damage energy release rate, Y + represents the tensile damage energy release rate, A + represents a parameter closely related to the descending section of the tensile stress-strain constitutive relationship, d - represents the compressive damage variable, represents the initial compressive damage energy release rate, Y - represents the compressive damage energy release rate, A - represents a parameter describing the stress softening effect of concrete materials before the uniaxial compressive peak stress, B - represents a parameter describing the softening effect occurring after the peak stress point, represents the tensile component of the effective stress tensor, E 0 represents the fourth-order elastic stiffness matrix of an isotropic material, K represents a material parameter considering the biaxial compression effect, represents the octahedral effective normal stress, represents the octahedral effective shear stress.

6. The method for analyzing the axial-flexural-shear coupling of a reinforced concrete rectangular hollow pier according to claim 2, characterized in that The expression of the plastic strain evolution data is: Among them, represents the plastic strain evolution data, and β str represents the material parameter introduced to control the rate and strength of plastic deformation. E0 represents the fourth-order elastic stiffness matrix of the isotropic material, σ represents the Cauchy stress, Ψ represents the total Helmholtz free energy of the damaged material, ε represents the total strain tensor, and d + represents the tensile damage variable, represents the first initial elastic free energy of the elastic damaged material, and ε e represents the elastic strain tensor, and d - represents the compressive damage variable, represents the second initial elastic free energy of the elastic damaged material, represents the tensile component of the effective stress tensor, represents the compressive component of the effective stress tensor, I represents the fourth-order unit tensor, and D represents the fourth-order damage tensor, represents the effective stress tensor, and E(d) represents the unloading stiffness of the material.

7. The method for axial-bending-shear coupling analysis of a reinforced concrete rectangular hollow pier according to claim 1, characterized in that, The S2 includes: Based on the plastic strain evolution data, divide the rectangular hollow pier of the elastoplastic damage constitutive model of reinforced concrete into an axial-bending region and an axial-shear region; Using fiber beam elements, simulate the mechanical behavior of the axial-bending region to obtain the discretized data of the axial-bending region; Using the membrane elements of the elastoplastic damage constitutive model, simulate the mechanical behavior of the axial-shear region to obtain the discretized data of the axial-shear region; By maintaining the degrees of freedom, coordinate the forces and deformations of the coincident nodes at the boundaries of the axial-bending region and the axial-shear region to obtain the discretized data of the boundary region; Integrate the discretized data of the axial-bending region, the discretized data of the axial-shear region, and the discretized data of the boundary region to obtain the discretized data.

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