Study on concentrated plastic hinge model of RC columns based on lateral stiffness

Abstract

The RC column concentrated plastic hinge model research method based on lateral stiffness relates to the structural seismic technology field; the method aims to solve the problem that the simulation precision of the existing concentrated plastic hinge model is influenced by the value of the multiplier n, and the function relationship between the spring rotation stiffness and the component lateral stiffness is established, without defining the multiplier n; the specific steps include deducing the concentrated plastic hinge series model unit stiffness matrix of the cantilever column, establishing the function relationship between the rotation stiffness and the lateral stiffness, designing the state updating algorithm based on the displacement loading control, verifying the accuracy of the new model, and comparing the precision of the existing model; the experimental results show that the simulation precision of the model is improved significantly, the nonlinear behavior of the RC column can be accurately simulated without the multiplier n, and the method has important practical significance; the method has been successfully applied to the seismic analysis of a plurality of typical RC frame structures, not only simplifies the calculation process, but also improves the calculation efficiency, provides a more reliable and convenient tool for the structural seismic design, and has high popularization value.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of structural seismic technology, and particularly relates to a concentrated plastic hinge model research method of RC column based on lateral stiffness. BACKGROUND

[0002] In the field of structural seismic technology, the reinforced concrete (RC) column as the main lateral force resisting member of RC frame structure, the accuracy and rationality of its nonlinear behavior simulation is crucial to the seismic design of RC frame structure. At present, the nonlinear analysis model of RC column component mainly includes concentrated plastic hinge model and distributed plastic model. Compared with the distributed plastic model, the concentrated plastic hinge model has been widely used in structural seismic design due to its high calculation efficiency, strong robustness and wide applicability.

[0003] The concentrated plastic hinge model is further divided into series model and parallel model; among them, the series model can accurately simulate the stiffness degradation, strength degradation and hysteresis curve pinch of RC column and a series of strong nonlinear behaviors, so most of the concentrated plastic hinge models are constructed based on the series model. The model divides the beam-column truss element into a series of components of end zero-length plastic rotational spring sub-element and middle elastic beam-column sub-element. By accurately defining the constitutive relationship of the end rotational spring (i.e. the moment-rotation relationship), the model can accurately simulate the nonlinear response of the RC column.

[0004] However, the existing lumped plasticity model still has some limitations in simulation accuracy, mainly manifested in that the simulation accuracy is controlled by the value of the multiplier "n". The root of this problem can be traced back to the research of Pacific Earthquake Engineering Research Center (PEER) in 2005. In their paper "Global collapse of frame structures under seismic excitations" in September 2005, they proposed to modify the stiffness of the rotational spring by defining the multiplier "n", which magnifies the rotational spring stiffness to "(n+1)" times of the component rotational stiffness, and magnifies the rotational stiffness of the elastic beam-column element to "(n+1) / n" times of the original. When n is 10, the simulation accuracy usually meets the requirements. Since then, many scholars have followed this method. For example, in the paper "A practical method for proper modeling of structural damping in inelastic plane structural systems" in the March 2010 issue of the journal "Computers & Structures", the multiplier "n" is used to modify the moment of inertia of the cross section of the elastic beam-column element, in order to match the moment-rotation angle hysteresis relationship measured by the test.

[0005] At the same time, some studies have shown that the journal "Journal of Structural Engineering" in April 2011 "Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading" used this method to establish a lumped plasticity model of a two-story steel frame based on the OpenSees finite element software; University of Colorado at Boulder in July 2011 "Implementation of Lumped Plasticity Models and Developments in an Object Oriented Nonlinear Finite Element Code" based on the above research results, through numerical simulation, it is concluded that when the multiplier "n" is 100, the simulation accuracy is more accurate than when n is 10.

[0006] Although the above method improves the simulation accuracy of the concentrated plastic hinge model to some extent, the value of the multiplier "n" becomes a parameter that needs to be set artificially, and its value directly affects the final structure nonlinear analysis result. Therefore, in order to overcome this limitation, it is necessary to deeply study the numerical modeling method of the series system of the end zero-length rotational spring unit and the elastic beam column unit, so as to establish a concentrated plastic hinge model of RC column which does not depend on the value of the multiplier "n" and can more accurately simulate the nonlinear behavior of the RC column.

[0007] Based on this background, the present application provides a concentrated plastic hinge model research method of RC column based on lateral stiffness, which aims to realize the accurate simulation of the nonlinear behavior of RC column without defining the multiplier "n" by constructing the functional relationship between the nonlinear rotational stiffness of the spring and the lateral stiffness of the column. SUMMARY

[0008] The technical problem to be solved by the present application is to provide a concentrated plastic hinge model research method of RC column based on lateral stiffness, which aims to accurately simulate the nonlinear behavior of RC column without defining the multiplier "n" by establishing the functional relationship between the nonlinear rotational stiffness of the spring and the lateral stiffness of the column obtained from the column test force-displacement hysteretic relationship.

[0009] To solve the above technical problems, the technical scheme adopted by the present application is a concentrated plastic hinge model research method of RC column based on lateral stiffness, comprising the following steps:

[0010] Step 1: Derive the element stiffness matrix of the concentrated plastic hinge series model of the cantilever column;

[0011] Step 2: According to the derived element stiffness matrix, establish the functional relationship between the rotational stiffness of the zero-length rotational spring and the lateral stiffness of the component;

[0012] Step 3: State updating algorithm of RC column concentrated plastic hinge model based on displacement loading control;

[0013] Step 4: Collect the test data of the existing test column, simulate the hysteretic curve of the column based on the RC column concentrated plastic hinge model constructed by the updating algorithm of Step 3, obtain the accuracy evaluation index of the simulation result, and verify the accuracy of the RC column concentrated plastic hinge model;

[0014] Step 5: Simulate the hysteretic curve of the column using the existing model, and the simulation accuracy is controlled by the multiplier n. Compare the simulation accuracy of the existing model and the RC column concentrated plastic hinge model.

[0015] In the preferred solution, the theoretical basis for deriving the element stiffness matrix in Step 1 is to derive the element stiffness matrix of the cantilever column concentrated plastic hinge series model based on the mechanical relationship and geometric analysis of the cantilever column element with two end rigid nodes and the cantilever column element with one end zero-length rotational spring , which is as follows:

[0016] (1)

[0017] wherein E, I, A, L represent the elastic modulus, moment of inertia, cross-sectional area, and length of the cantilever column, respectively; is the rotational stiffness of the spring; , is a user-defined parameter, and its definition is as follows:

[0018] (2).

[0019] In the preferred solution, the theoretical basis for the functional relationship between the rotational stiffness of the rotational spring and the lateral stiffness of the member in Step 2 is to establish the specific functional relationship between the rotational stiffness of the spring and the lateral stiffness of the member , the incremental rotation angle of the free end , and the incremental horizontal displacement based on the element stiffness matrix of the cantilever column concentrated plastic hinge model derived above, through the mechanical relationship and geometric boundary conditions of the model, and the specific formula is as follows:

[0020] (3).

[0021] In the preferred solution, in each iteration step, the state update algorithm in Step 3 maintains a constant displacement increment and updates the rotational stiffness of the spring and the stiffness matrix using the functional relationship in Step 2, to obtain the load increment factor , and determines the external load vector through the load factor .

[0022] In the preferred solution, the test data in Step 4 comes from the pseudo-static loading test data of a circular cross-section RC cantilever column on a certain official website, and the precision evaluation index of the simulation results is the coefficient of determination , the mean absolute error MAE (Mean Absolute Error), and the root mean squared error RMSE (Root Mean Squared Error).

[0023] In the preferred scheme, the existing model in Step 5 is compared and analyzed with the RC column concentrated plastic hinge model, by taking different values of the multiplier n, without modification, taking 10, taking 100, and comparing the simulation accuracy with the RC column concentrated plastic hinge model, to verify that the RC column concentrated plastic hinge model can achieve higher simulation accuracy without defining the multiplier n.

[0024] The RC column concentrated plastic hinge model based on lateral stiffness provided by the application has the following beneficial effects:

[0025] 1. The application overcomes and solves the problem that the simulation accuracy of the existing concentrated plastic hinge model is highly dependent on the value of the multiplier "n", and different values directly affect the results of the structural nonlinear analysis, and the existing model has the problem of insufficient simulation of the stiffness degradation, strength degradation and pinching of the hysteretic curve of the RC column.

[0026] 2. The application performs low-cycle cyclic loading nonlinear analysis on three groups of RC columns with bending failure, shear failure and bending-shear failure by using the existing concentrated plastic hinge model, and compares the analysis results with the test data, and finds that the multiplier "n" in the existing concentrated plastic hinge model has a greater impact on the simulation accuracy, and when n is 100, the simulation result is more accurate than when n is 10.

[0027] 3. The application takes an RC cantilever column as an example and proposes a new method that only depends on the lateral stiffness of the column. Based on the new method, the total element stiffness matrix of the elastic beam column sub-unit connected with the rotational spring sub-unit at one end is derived, and a functional relationship between the nonlinear rotational stiffness of the spring and the lateral stiffness of the column obtained from the column test force-displacement hysteretic relationship is established, and then the rotational stiffness of the elastic beam column sub-unit and the rotational spring sub-unit is not modified by the multiplier "n".

[0028] 4. Compared with the existing concentrated plastic hinge model, the new model proposed by the application does not need to define the multiplier "n". Moreover, the same group of RC columns with bending failure, shear failure and bending-shear failure is analyzed by using the new model, and the analysis results are compared with the test data, and it is found that the simulation results obtained by the new model are more accurate than those obtained by the existing concentrated plastic hinge model, and the simulation accuracy is improved.

[0029] 5. The application eliminates the dependence on the multiplier "n", and the traditional concentrated plastic hinge model needs to define the multiplier "n" to adjust the stiffness of the rotational spring and the elastic beam column sub-unit to achieve higher simulation accuracy. However, the value of the multiplier "n" is uncertain, which may directly affect the accuracy of the simulation results. The scheme successfully eliminates the dependence on the multiplier "n" by establishing a direct functional relationship between the rotational stiffness of the spring and the lateral stiffness of the component, making the model more perfect and accurate in theory.

[0030] 6、Compared with the existing model, the new model proposed by the scheme has a significant improvement in simulation accuracy. Through comparison of test data and simulation results, it can be found that the new model is superior to the existing model in terms of precision evaluation indexes such as determination coefficient R2, mean absolute error MAE and root mean square error RMSE, which shows that the new model can more accurately simulate the nonlinear behavior of RC columns and has higher practicability and reliability.

[0031] 7、The new model of the application has higher robustness and applicability, and can be widely applied in the seismic design of RC frame structures, providing more reliable reference for engineers.

[0032] 8、The research results of the application not only solve the problems existing in the existing model, but also provide a new idea and method for the research of RC column nonlinear analysis model, and promote the development of the field of structural seismic technology.

[0033] 9、The method of the application has been successfully applied in the seismic analysis of a plurality of typical RC frame structures, not only simplifying the calculation process, but also improving the calculation efficiency, providing a more reliable and convenient tool for structural seismic design, and is expected to further promote the development of structural seismic research. BRIEF DESCRIPTION OF DRAWINGS

[0034] The application will be further described below in combination with the drawings and implementation examples:

[0035] Figure 1 is the technical roadmap of the application;

[0036] Figure 2 is the flowchart of the displacement control nonlinear iterative algorithm of the application based on the lateral stiffness updated spring plastic rotation stiffness;

[0037] Figure 3 is the mechanical relationship and geometric relationship of the zero-length rotational spring subunit and the elastic beam column subunit connected in series in embodiment 2 of the application;

[0038] Figure 4 is the cantilever column concentrated plastic hinge series connection model in embodiment 2 of the application;

[0039] Figure 5 is the comparison chart of the test simulation results and test data of the bending failure column column 1 in embodiment 2 of the application;

[0040] Figure 6 is the comparison chart of the test simulation results and test data of the shear failure column column 2 in embodiment 2 of the application;

[0041] Figure 7 is the comparison chart of the test simulation results and test data of the bending shear failure column column 3 in embodiment 2 of the application.​ DETAILED DESCRIPTION

[0042] The technical solutions in the present application are further described below in combination with the drawings and examples:

[0043] Example 1

[0044] As shown in the following steps, the RC column concentrated plastic hinge model research method based on lateral stiffness comprises the following steps: Figures 1-2

[0045] Step 1: Derivation of the element stiffness matrix of the cantilever column concentrated plastic hinge series model;

[0046] Step 2: According to the derived element stiffness matrix, the function relationship between the rotational stiffness of the zero-length rotational spring and the lateral stiffness of the component is established;

[0047] Step 3: State updating algorithm of RC column concentrated plastic hinge model based on displacement loading control;

[0048] Step 4: Collect the test data of the existing test column, simulate the hysteresis curve of the column based on the state updating algorithm of the RC column concentrated plastic hinge model, obtain the accuracy evaluation index of the simulation result, and verify the accuracy of the RC column concentrated plastic hinge model;

[0049] Step 5: Simulate the hysteresis curve of the column using the existing model, and the simulation accuracy is controlled by the multiplier n. Compare the simulation accuracy of the existing model and the RC column concentrated plastic hinge model.

[0050] In this embodiment, the theoretical basis for deriving the element stiffness matrix in Step 1 is based on the mechanical relationship and geometric analysis of the cantilever column element with two rigid nodes and the cantilever column element with a zero-length rotational spring at one end, and the element stiffness matrix of the cantilever column concentrated plastic hinge series model is derived as follows:

[0051] (1)

[0052] Wherein, E, I, A, L respectively represent the elastic modulus, moment of inertia, cross-sectional area and length of the cantilever column; is the rotational stiffness of the spring; , is a self-defined parameter, and its self-definition is as follows:

[0053] (2).

[0054] ​​Further, the theoretical basis of the function relationship between the rotational stiffness of the rotating spring in Step 2 and the lateral stiffness of the member is that, based on the unit stiffness matrix of the cantilever column concentrated plastic hinge model derived above, the rotational stiffness of the spring is established by the mechanical relationship and geometric boundary conditions of the model and the lateral stiffness of the member , the specific function relationship of the free end rotation angle increment and the horizontal displacement increment is as follows:

[0055] (3).

[0056] Further, in Step 3, the state updating algorithm maintains a constant displacement increment in each iteration step, and updates the spring rotational stiffness and stiffness matrix using the function relationship in Step 2, to obtain the load increment factor , and determines the external load vector by the load factor .

[0057] Further, the test data in Step 4 comes from the pseudo-static loading test data of a circular cross-section RC cantilever column on a certain website, and the precision evaluation index of the simulation result is the coefficient of determination , the mean absolute error MAE and the root mean square error RMSE.

[0058] Further, in Step 5, the existing model is compared with the RC column concentrated plastic hinge model by taking different values of the multiplier n, i.e. not modifying, taking 10, and taking 100, to compare the simulation accuracy with the RC column concentrated plastic hinge model, and to verify that the RC column concentrated plastic hinge model can achieve higher simulation accuracy without defining the multiplier n.

[0059] Embodiment 2

[0060] In another preferred embodiment, based on the above-mentioned embodiment 1, as shown in Figures 1-2 , the RC column concentrated plastic hinge model research method based on lateral stiffness comprises the following steps:

[0061] Step 1: Derive the unit stiffness matrix of the cantilever column concentrated plastic hinge series model;

[0062] Step 2: Establish the function relationship between the rotational stiffness of the zero-length rotating spring and the lateral stiffness of the member according to the derived unit stiffness matrix;

[0063] Step 3: RC column concentrated plastic hinge model state updating algorithm based on displacement loading control;

[0064] Step 4: Collect the experimental data of existing test columns, simulate the hysteresis curve of the column using the RC column concentrated plastic hinge model constructed based on the above state update algorithm, obtain the accuracy evaluation index of the simulation results, and verify the RC column concentrated plastic hinge model. Figure 1 The accuracy of the model (hereinafter referred to as the model in this paper);

[0065] Step 5: Simulate the hysteresis curve of the column using the existing model (the simulation accuracy is controlled by the multiplier "n"), and compare the simulation accuracy of the existing model with that of the RC column concentrated plastic hinge model.

[0066] The theoretical basis for deriving the element stiffness matrix in Step 1 is based on the mechanical relationship and geometric analysis between a cantilever column element with rigid nodes at both ends and a cantilever column element with a zero-length rotational spring at one end, thus deriving the element stiffness matrix of the cantilever column concentrated plastic hinge series model. See details Figure 3 Japanese (1):

[0067] (1)

[0068] Where E, I, A, and L represent the elastic modulus, moment of inertia, cross-sectional area, and length of the cantilever column, respectively. Let be the rotational stiffness of the spring; , For custom parameters, only for the simplified formula (1), the specific definition is shown in formula (2):

[0069] (2).

[0070] The theoretical basis for the functional relationship between the rotational stiffness of the spring and the lateral stiffness of the component in Step 2 is based on the element stiffness matrix of the concentrated plastic hinge model of the cantilever column derived above. The rotational stiffness of the spring is established through the mechanical relationships and geometric boundary conditions of this model. With the lateral stiffness of the component Free end rotation increment Horizontal displacement increment The specific functional relationship; and This represents the force and displacement vectors at points 1 and 3 (i.e., the outer ends of the rotational spring) of a cantilever column element acting on a zero-length rotational spring in a concentrated plastic hinge model; see modeling diagram for details. Figure 4 The plastic hinge is simulated using a zero-length rotational spring; the specific derivation process is as follows:

[0071] Because the transformation angle from the local coordinate system to the global coordinate system is =-90°, substitute it into the transformation matrix The element stiffness matrix in the global coordinate system can be obtained. :

[0072] (4)

[0073] (5)

[0074] (6)

[0075] where, is the transformation matrix, is the transpose matrix of the transformation matrix, is the transformation angle.

[0076] Element force increment vector in global coordinate system :

[0077] (7)

[0078] (8)

[0079] where, respectively represent the force increment acting on the 1st and 3rd nodes in (d), Figure 4 is the force increment vector in local coordinate system. Element displacement increment vector in global coordinate system

[0080] :

[0081] (9)

[0082] (10)

[0083] where, respectively represent the displacement increment acting on the 1st and 3rd nodes in (d), Figure 4 is the displacement increment vector in local coordinate system. The matrix relationship in global coordinate system is obtained as follows:

[0084]

[0085] (11). In the established cantilever column concentrated plastic hinge model, the fixed end nodes of the zero-length rotational spring element and the elastic beam-column element connected with the ground are represented by two points, which represent the same point. Therefore, this point cannot change in displacement, i.e. the boundary condition needs to be satisfied:

[0086] Therefore, formula (11) can be simplified as:

[0087] (12)

[0088] respectively represent​​Figure 4 (d) the displacement increment of node 1, respectively represent Figure 4 (d) the force increment of node 1;

[0089] the shear increment in formula (12) and the horizontal displacement increment are in an equation relationship, and the equation is:

[0090] (13)

[0091] Lateral stiffness of the cantilever column:

[0092] (14)

[0093] Solving formula (2), (13) and (14) simultaneously, the rotational spring stiffness is:

[0094] (3)

[0095] wherein, represents Figure 4 (d) the horizontal displacement increment of node 1, represents Figure 2 (d) the shear increment of node 1; is expressed as the lateral stiffness of the column.

[0096] The displacement loading control-based RC column concentrated plastic hinge model state updating algorithm in Step 3 is specifically that the known displacement increment is applied to the corresponding degree of freedom, and is kept constant in each iteration step, and the spring rotational stiffness and stiffness matrix are updated based on formula (3) and (6), and the load increment factor is obtained therefrom; the load increment factor is a variable calculated during the balance iteration, and the external load vector is determined by the load factor , and the detailed steps are shown in Figure 5 .

[0097] The model verification and comparative analysis of Step 4 and Step 5 are as follows: the column test data come from the round-section RC cantilever column pseudo-static loading test data on the PEER Structural Performance Database website, and the test data of the bending failure, shear failure and bending-shear failure columns are respectively referred to as column 1, column 2 and column 3; the horizontal displacement in the test data is brought into the displacement loading control-based RC column concentrated plastic hinge model state updating algorithm to obtain the corresponding base shear, and the simulation results of the RC column concentrated plastic hinge model are compared with the simulation results of the existing model. The numerical experiment is divided into four working conditions:

[0098] (1) Elastic beam-column element stiffness and spring rotational stiffness are not modified by the multiplier "n" (referred to as "existing model unmodified");

[0099] (2) The multiplier "n" is taken as 10 (referred to as "existing model n=10");

[0100] (3) The multiplier "n" is taken as 100 (referred to as "existing model n=100");

[0101] (4) The new method is used for modeling analysis (referred to as "RC column concentrated plastic hinge model");

[0102] The comparison of four working conditions , MAE, RMSE, Figure 6 , Figure 7 , ​ The comparison of simulation results of existing model and RC column concentrated plastic hinge model (referred to as the model in this paper) and test data is shown in the figure; the specific results are shown in Table 1:

[0103] Table 1 Evaluation index of existing model and RC column concentrated plastic hinge model (referred to as the model in this paper)

[0104]

[0105] Table 1 shows the performance index of the existing concentrated plastic hinge model in the proper modification of the elastic rod rotational stiffness and the spring rotational stiffness. In Table 1, when n is taken as 10 and n is taken as 100, the simulation results have high consistency with the hysteresis curves of the three groups of test columns. Among them, for the bending failure column (column 1), the shear failure column (column 2), and the bending shear failure column (column 3), the of n taken as 10 and n taken as 100 are higher than that of the unmodified multiplier "n" working condition (i.e. the existing model unmodified working condition), and the MAE and RMSE are lower than those of the existing model unmodified working condition. In addition, when n is taken as 100, the simulation accuracy of the existing model is higher than that when n is taken as 10, which is consistent with the discussion in the foregoing. For the same group of bending failure column, shear failure column and bending shear failure column, the column hysteresis curves simulated by the RC column concentrated plastic hinge model are highly consistent with the corresponding test data. Moreover, compared with the results obtained by the existing model, the RC column concentrated plastic hinge model is superior to the existing model in , MAE and RMSE three simulation accuracy evaluation indexes; which further verifies the accuracy and reliability of the RC column concentrated plastic hinge model.

[0106] In the preferred scheme, in each iteration step, the state update algorithm in Step 3 maintains a constant displacement increment, and updates the spring rotational stiffness and the stiffness matrix by using the functional relationship in Step 2, so as to obtain the load increment factor and the load factor is determined by determining the external load vector; the above settings ensure the stability and convergence of the algorithm, while improving the calculation efficiency; in the iteration process, the convergence criterion is dynamically adjusted to accurately control the balance between calculation accuracy and resource consumption.

[0107] In the preferred scheme, the test data in Step 4 is derived from the circular cross-section RC cantilever column pseudo-static loading test data of a certain official website, and the precision evaluation index of the simulation result is the coefficient of determination , mean absolute error MAE and root mean square error RMSE; the above settings ensure high consistency between the simulation process and the real test data, and through evaluation of the model prediction ability, MAE and RMSE quantify the error range, providing solid data support for structural safety evaluation.

[0108] In the preferred scheme, the existing model in Step 5 is compared with the RC column concentrated plastic hinge model, and by taking different values of the multiplier n, the simulation accuracy is compared with the RC column concentrated plastic hinge model without defining the multiplier n, which can achieve higher simulation accuracy; the above settings not only reduce the complexity of parameter setting under the same experimental conditions, but also significantly improve the prediction accuracy, proving the advantages of the RC column concentrated plastic hinge model in improving simulation accuracy and simplifying model complexity.

[0109] In summary, the RC column concentrated plastic hinge model research method based on lateral stiffness provided by the application solves the problems that the simulation accuracy of the existing concentrated plastic hinge series model is controlled by the value of the multiplier "n" and the nonlinear behavior of the column is simulated by the actual column lateral stiffness and the spring rotation stiffness; the reliability and accuracy of the RC column concentrated plastic hinge model research method based on lateral stiffness are verified through comparative analysis of the existing model, which has important practical significance for establishing an accurate and reasonable RC column nonlinear analysis model; the RC column concentrated plastic hinge model research method based on lateral stiffness is first proposed, which is completely different from the previous method of adjusting the rotation spring stiffness and the elastic beam column element stiffness by relying on the multiplier "n"; the new method directly relates the rotation stiffness of the spring and the lateral stiffness of the component, and establishes a more direct and accurate simulation method; the application deduces the element stiffness matrix of the cantilever column concentrated plastic hinge series model through mechanical relationship and geometric analysis, and establishes the specific functional relationship between the rotation stiffness of the zero-length rotary spring and the lateral stiffness of the component, which makes the new model more rigorous and novel in theory; the scheme of the application proposes a RC column concentrated plastic hinge model state updating algorithm based on displacement loading control, which updates the spring rotation stiffness and stiffness matrix in real time according to the displacement increment in the iteration process, so as to ensure that the model can accurately simulate the nonlinear behavior of the RC column under different loading conditions; the successful proposal of the scheme not only provides a new idea and method for the construction of the RC column nonlinear analysis model, but also makes an important contribution to the technical progress in the field of structural seismic design; through in-depth research and analysis, the scheme provides a beneficial reference for the development and optimization of similar models in the future; at the same time, the research results have broad application prospects, and can be expected to play an important role in complex engineering fields such as high-rise buildings, bridges and large-span structures, improve the safety and economy of structural design, and promote the continuous innovation and development of engineering technology.

Claims

1. A research method for a concentrated plastic hinge model of an RC column based on lateral stiffness, characterized in that, Includes the following steps: Step 1: Derive the element stiffness matrix of the cantilever column concentrated plastic hinge series model. The theoretical basis is the mechanical relationship and geometric analysis of the cantilever column element with rigid nodes at both ends and the cantilever column element with a zero-length rotational spring at one end, to derive the element stiffness matrix of the cantilever column concentrated plastic hinge series model. The details are as follows: （1） Where E, I, A, and L represent the elastic modulus, moment of inertia, cross-sectional area, and length of the cantilever column, respectively. Let be the rotational stiffness of the spring; , These are custom parameters, and their definitions are as follows: （2）； Step 2: Based on the derived element stiffness matrix, establish the functional relationship between the rotational stiffness of the zero-length rotational spring and the lateral stiffness of the component. The theoretical basis is the element stiffness matrix of the cantilever column concentrated plastic hinge series model derived in Step 1. Through the mechanical relationships and geometric boundary conditions of this model, the rotational stiffness of the spring is established. With the lateral stiffness of the component Free end rotation increment Horizontal displacement increment The specific functional relationship and formula are as follows: （3）； Step 3: State update algorithm for RC column concentrated plastic hinge model based on displacement loading control; Step 4: Collect the experimental data of existing test columns, and simulate the hysteresis curve of the RC column concentrated plastic hinge model constructed based on the algorithm updated in Step 3. Obtain the accuracy evaluation index of the simulation results and verify the accuracy of the RC column concentrated plastic hinge model. Step 5: Simulate the hysteresis curve of the column using the existing model. The simulation accuracy is controlled by the multiplier n. Compare the simulation accuracy of the existing model with that of the RC column concentrated plastic hinge model.

2. The research method for the concentrated plastic hinge model of an RC column based on lateral stiffness according to claim 1, characterized in that: Step 3, based on the displacement-load-controlled RC column concentrated plastic hinge model state update algorithm, maintains a constant displacement increment in each iteration step and updates the spring rotational stiffness and stiffness matrix using the functional relationship from Step 2, thereby obtaining the load increment factor. and through load factor Determine the external load vector.

3. The research method for the concentrated plastic hinge model of an RC column based on lateral stiffness according to claim 1, characterized in that: The experimental data in Step 4 comes from the quasi-static loading test data of the circular cross-section RC cantilever column, and the accuracy evaluation index of the simulation results adopts the coefficient of determination. Mean absolute error (MAE) and root mean square error (RMSE).

4. The research method for the concentrated plastic hinge model of an RC column based on lateral stiffness according to claim 1, characterized in that: The existing model in Step 5 is compared and analyzed with the RC column concentrated plastic hinge model. By taking different values ​​of the multiplier n, namely without correction, taking 10, and taking 100, the simulation accuracy is compared with that of the RC column concentrated plastic hinge model. This verifies that the RC column concentrated plastic hinge model can achieve higher simulation accuracy without defining the multiplier n.

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