Novel RC column concentrated plastic hinge model research method based on lateral rigidity

Abstract

The invention discloses a novel RC column concentrated plastic hinge model research method based on lateral rigidity, and relates to the technical field of structural seismic resistance. The method aims at solving the problem that the simulation precision of an existing concentrated plastic hinge model is affected by the value of a multiplier n, and the multiplier n does not need to be defined by establishing the function relation between the spring rotation rigidity and the component lateral rigidity; the method comprises the specific steps of deducing a unit stiffness matrix of the cantilever column concentrated plastic hinge series model, establishing a function relationship between rotational stiffness and lateral stiffness, designing a state updating algorithm based on displacement loading control, verifying the accuracy of a new model, and comparing the accuracy of the new model with the accuracy of an existing model. Experimental results show that the model simulation precision is remarkably improved, the nonlinear behavior of the RC column can be accurately simulated without a multiplier n, and the method has important practical significance; the method is successfully applied to anti-seismic analysis of a plurality of typical RC frame structures, the calculation process is simplified, the calculation efficiency is improved, a more reliable and convenient tool is provided for structural anti-seismic design, and the popularization value is high.

Description

Technical Field

[0001] The invention relates to the technical field of structural earthquake resistance, and in particular to a research method for a novel RC column concentrated plastic hinge model based on lateral stiffness. Background Art

[0002] In the field of structural seismic technology, reinforced concrete (RC) columns are the main lateral force-resisting components of RC frame structures. The accuracy and rationality of their nonlinear behavior simulation are crucial to the seismic design of RC frame structures. At present, the nonlinear analysis models of RC column components are mainly divided into two categories: 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 advantages such as high computational efficiency, strong robustness and wide applicability.

[0003] The concentrated plastic hinge model is further divided into a series model and a parallel model; among them, the series model can accurately simulate a series of strong nonlinear behaviors of RC columns, such as stiffness degradation, strength degradation, and hysteresis curve pinching. Therefore, most concentrated plastic hinge models are built based on the series model. This model divides the beam-column bar system unit into a series component of the end zero-length plastic rotation spring subunit and the middle elastic beam-column subunit. By accurately defining the constitutive relationship of the end rotation spring (i.e., the moment-chord rotation relationship), the model can more accurately simulate the nonlinear response of the RC column.

[0004] However, the existing concentrated plastic hinge series model still has certain limitations in simulation accuracy, mainly manifested in that its 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 article "Global collapse of frame structures under seismic excitations" in September 2005, they proposed to modify the stiffness of the rotation spring by defining the multiplier "n", amplifying the stiffness of the rotation spring to "(n+1)" times the rotation stiffness of the component, and amplifying the rotation stiffness of the elastic beam-column unit to the original "(n+1) / n" times, where n is 10, the simulation accuracy usually meets the requirements. Since then, many scholars have followed this method. For example, in the article “A practical method for proper modeling of structural damping in inelastic plane structural systems” published in the journal Computers & Structures in March 2010, it was proposed to use the multiplier “n” to correct the moment of inertia of the elastic beam-column unit section in order to match the moment-chord-rotation hysteresis relationship measured in the experiment.

[0005] At the same time, there are studies showing that the Journal of Structural Engineering used this method in its article “Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading” in April 2011 to establish a concentrated plastic hinge series model of a two-story steel frame based on the OpenSees finite element software; the University of Colorado at Boulder published its article “Implementation of Lumped Plasticity Models and Developments in an Object Oriented Nonlinear Finite Element Code” in July 2011, based on the above research results, and concluded through numerical simulation 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 a certain extent, the value of the multiplier "n" becomes a parameter that needs to be set manually, and its different values ​​will directly affect the final structural nonlinear analysis results. Therefore, in order to overcome this limitation, it is necessary to conduct in-depth research on the numerical modeling method of the end zero-length rotation spring unit and the elastic beam-column unit series system to establish a new concentrated plastic hinge model that is independent of the value of the multiplier "n" and can more accurately simulate the nonlinear behavior of RC columns.

[0007] It is based on this background that a new research method for concentrated plastic hinge model of RC columns based on lateral stiffness is proposed in this paper, which aims to achieve the goal of accurately simulating the nonlinear behavior of RC columns without defining the multiplier "n" by constructing a functional relationship between the nonlinear rotational stiffness of the spring and the lateral stiffness of the column. Summary of the invention

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

[0009] In order to solve the above technical problems, the technical solution adopted by the present invention is a new RC column concentrated plastic hinge model research method based on lateral stiffness, which includes the following steps: Step 1: Derive the unit stiffness matrix of the cantilever column concentrated plastic hinge series model; Step 2: Based on the derived element stiffness matrix, establish the functional relationship between the rotational stiffness of the zero-length rotation spring and the lateral stiffness of the component; Step 3: A new state updating algorithm for concentrated plastic hinge model of RC columns based on displacement loading control; Step 4: Collect the test data of the existing test columns, and construct the new RC column concentrated plastic hinge model based on the state update algorithm to simulate the hysteresis curve of the column, obtain the accuracy evaluation index of the simulation results, and verify the accuracy of the model in this paper; Step 5: Use the existing concentrated plastic hinge model to simulate the hysteresis curve of the column. The simulation accuracy is controlled by the multiplier n. Compare the simulation accuracy of the existing model and the model proposed in this paper.

[0010] In the preferred solution, the theoretical basis for deriving the unit stiffness matrix in step 1 is to derive the unit stiffness matrix of the cantilever column concentrated plastic hinge series model based on the mechanical relationship and geometric analysis of the cantilever column unit with rigid nodes at both ends and the cantilever column unit with zero-length rotation spring at one end. , as follows: (1) Among them, E, I, A, and L represent the elastic modulus, moment of inertia, cross-sectional area, and rod length of the cantilever column, respectively; is the rotational stiffness of the spring; , are custom parameters, and their definitions are as follows: (2).

[0011] In the preferred solution, the theoretical basis for the functional relationship between the rotational stiffness of the rotation spring and the lateral stiffness of the component in Step 2 is to establish the rotational stiffness of the spring through the mechanical relationship and geometric boundary conditions of the model based on the unit stiffness matrix of the cantilever column concentrated plastic hinge model derived above. The lateral stiffness of the member , free end angle increment , horizontal displacement increment The specific functional relationship of is as follows: (3).

[0012] In the preferred embodiment, the state update algorithm in Step 3 obtains the load increment factor by maintaining a constant displacement increment in each iteration step and updating the spring rotation stiffness and stiffness matrix using the functional relationship in Step 2. , and determine the external load vector through the load factor.

[0013] In the preferred solution, the test data in Step 4 is derived from the quasi-static loading test data of a circular cross-section RC cantilever column of a certain official website, and the accuracy evaluation index of the simulation result adopts the determination coefficient , mean absolute error MAE (Mean Absolute Error) and root mean square error RMSE (Root Mean Squared Error).

[0014] In the preferred solution, the existing model in Step 5 is compared and analyzed with the model in this paper. By taking different values ​​of the multiplier n, namely no correction, 10, and 100, the simulation accuracy is compared with the model in this paper to verify that the model in this paper can achieve higher simulation accuracy without defining the multiplier n.

[0015] The novel RC column concentrated plastic hinge model research method based on lateral stiffness provided by the present invention has the following beneficial effects: 1. The present invention 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 structural nonlinear analysis, and the existing model is insufficient in simulating strong nonlinear behaviors such as stiffness degradation, strength degradation and hysteresis curve pinching of RC columns; 2. The present invention adopts the existing concentrated plastic hinge model to carry out low-cycle reciprocating loading nonlinear analysis on three groups of RC columns with bending failure, shear failure and bending-shear failure, and compares the analysis results with the test data. It is found that the multiplier "n" in the existing concentrated plastic hinge model has a great influence on the simulation accuracy. When n is 100, the simulation result is more accurate than when n is 10; 3. Taking the RC cantilever column as an example, the present invention proposes a new method that only relies on the lateral stiffness of the column. Based on the new method, the total unit stiffness matrix formed by connecting one end of the elastic beam-column subunit in series with the rotation spring subunit is derived, and the functional relationship between the nonlinear rotation stiffness of the spring and the column lateral stiffness obtained from the column test force-displacement hysteresis relationship is established, thereby eliminating the need to use the rotation stiffness of the column bending moment-chord angle hysteresis relationship, and eliminating the need to perform additional corrections to the stiffness of the elastic beam-column subunit and the rotation spring subunit using the multiplier "n"; 4. Compared with the existing concentrated plastic hinge model, the new model proposed in the present invention does not need to define the multiplier "n". Moreover, the new model is used to perform nonlinear analysis on the same group of RC columns with bending failure, shear failure, and bending-shear failure, and the results of the analysis are compared with the test data. 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, which improves the simulation accuracy; 5. The present invention eliminates the reliance on the multiplier "n". The traditional concentrated plastic hinge model needs to define the multiplier "n" to adjust the stiffness of the rotation spring and the elastic beam-column 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. This solution successfully eliminates the reliance on the multiplier "n" by establishing a direct functional relationship between the spring rotation stiffness and the lateral stiffness of the component, making the model more complete and accurate in theory. 6. Compared with the existing model, the new model proposed in this scheme has significantly improved the simulation accuracy. By comparing the test data and simulation results, it can be found that the new model has a higher determination coefficient. The accuracy evaluation indicators such as mean absolute error (MAE) and root mean square error (RMSE) are better than those of the existing models, which shows that the new model can simulate the nonlinear behavior of RC columns more accurately and has higher practicality and reliability. 7. The new model of the present invention has higher robustness and applicability, and can be widely used in the seismic design of RC frame structures, providing engineers with a more reliable reference basis; 8. The research results of the present invention not only solve the problems existing in the existing models, but also provide new ideas and methods for the research of nonlinear analysis models of RC columns, and promote the development of the field of structural seismic technology; 9. The method of the present invention has been successfully applied to the seismic analysis of a number of typical RC frame structures, which not only simplifies the calculation process, but also improves the calculation efficiency, provides 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 THE DRAWINGS

[0016] The present invention will be further described below in conjunction with the accompanying drawings and implementation examples: Figure 1 It is the technical roadmap of the present invention; Figure 2 The present invention is a flow chart of a displacement-controlled nonlinear iterative algorithm for updating the plastic rotational stiffness of a spring based on lateral stiffness; Figure 3 The mechanical relationship and geometric relationship of the zero-length rotation spring subunit and the elastic beam-column subunit connected in series in Example 2 of the present invention; Figure 4 This is the cantilever column concentrated plastic hinge series model of Example 2 of the present invention; Figure 5 This is a comparison chart of the test simulation results and test data of the bending failure column 1 of Example 2 of the present invention; Figure 6 This is a comparison chart of the test simulation results and test data of the shear failure column 2 of Example 2 of the present invention; Figure 7 This is a comparison chart between the test simulation results and the test data of the bending-shear failure column 3 of Example 2 of the present invention. DETAILED DESCRIPTION

[0017] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments: Example 1 like Figure 1~2 As shown in the figure, the new RC column concentrated plastic hinge model research method based on lateral stiffness includes the following steps: Step 1: Derive the unit stiffness matrix of the cantilever column concentrated plastic hinge series model; Step 2: Based on the derived element stiffness matrix, establish the functional relationship between the rotational stiffness of the zero-length rotation spring and the lateral stiffness of the component; Step 3: A new state updating algorithm for concentrated plastic hinge model of RC columns based on displacement loading control; Step 4: Collect the test data of the existing test columns, and construct the new RC column concentrated plastic hinge model based on the state update algorithm to simulate the hysteresis curve of the column, obtain the accuracy evaluation index of the simulation results, and verify the accuracy of the model in this paper; Step 5: Use the existing concentrated plastic hinge model to simulate the hysteresis curve of the column. The simulation accuracy is controlled by the multiplier n. Compare the simulation accuracy of the existing model and the model proposed in this paper.

[0018] In this embodiment, the theoretical basis for deriving the unit stiffness matrix in step 1 is to derive the unit stiffness matrix of the cantilever column concentrated plastic hinge series model based on the mechanical relationship and geometric analysis of the cantilever column unit with rigid nodes at both ends and the cantilever column unit with zero-length rotation spring at one end. , as follows: (1) Among them, E, I, A, and L represent the elastic modulus, moment of inertia, cross-sectional area, and rod length of the cantilever column, respectively; is the rotational stiffness of the spring; , are custom parameters, and their definitions are as follows: (2).

[0019] Furthermore, the theoretical basis for the functional relationship between the rotational stiffness of the rotation spring and the lateral stiffness of the component in Step 2 is to establish the rotational stiffness of the spring through the mechanical relationship and geometric boundary conditions of the model based on the unit stiffness matrix of the cantilever column concentrated plastic hinge model derived in the previous article. The lateral stiffness of the member , free end angle increment , horizontal displacement increment The specific functional relationship of is as follows: (3).

[0020] Furthermore, the state update algorithm in Step 3 obtains the load increment factor by maintaining a constant displacement increment in each iteration step and updating the spring rotation stiffness and stiffness matrix using the functional relationship in Step 2. , and determine the external load vector through the load factor.

[0021] Furthermore, the test data in Step 4 is derived from the quasi-static loading test data of a circular cross-section RC cantilever column of a certain official website, and the accuracy evaluation index of the simulation result adopts the determination coefficient , mean absolute error MAE and root mean square error RMSE.

[0022] Furthermore, the existing model in Step 5 is compared and analyzed with the model in this paper. By taking different values ​​of the multiplier n, namely no correction, 10, and 100, the simulation accuracy is compared with the model in this paper, verifying that the model in this paper can achieve higher simulation accuracy without defining the multiplier n.

[0023] Example 2 In another preferred embodiment, based on the above embodiment 1, Figure 1~2 As shown in the figure, the new RC column concentrated plastic hinge model research method based on lateral stiffness includes the following steps: Step 1: Derive the unit stiffness matrix of the cantilever column concentrated plastic hinge series model; Step 2: Based on the derived element stiffness matrix, establish the functional relationship between the rotational stiffness of the zero-length rotation spring and the lateral stiffness of the component; Step 3: A new state updating algorithm for concentrated plastic hinge model of RC columns based on displacement loading control; Step 4: Collect the test data of the existing test columns, and construct the new RC column concentrated plastic hinge model based on the state update algorithm to simulate the hysteresis curve of the column, obtain the accuracy evaluation index of the simulation results, and verify the accuracy of the model in this paper; Step 5: Use the existing concentrated plastic hinge model to simulate the hysteresis curve of the column (the simulation accuracy is controlled by the multiplier "n"), and compare the simulation accuracy of the existing model and the model proposed in this paper.

[0024] The theoretical basis for deriving the unit stiffness matrix in step 1 is to derive the unit stiffness matrix of the cantilever column concentrated plastic hinge series model based on the mechanical relationship and geometric analysis of the cantilever column unit with rigid nodes at both ends and the cantilever column unit with zero-length rotation spring at one end. , see Figure 3 And formula (1): (1) Among them, E, I, A, and L represent the elastic modulus, moment of inertia, cross-sectional area, and rod length of the cantilever column, respectively; is the rotational stiffness of the spring; , It is a custom parameter, which is only used to simplify formula (1). The specific definition is shown in formula (2): (2).

[0025] The theoretical basis for the functional relationship between the rotational stiffness of the rotation spring and the lateral stiffness of the component in Step 2 is to establish the rotational stiffness of the spring through the mechanical relationship and geometric boundary conditions of the model based on the unit stiffness matrix of the cantilever column concentrated plastic hinge model derived in the previous article. The lateral stiffness of the member , free end angle increment , horizontal displacement increment The specific functional relationship of and Represents the force vector and displacement vector at the first and third points (i.e., the outer end of the rotation spring) of the cantilever column element with a zero-length rotation spring at the end in the concentrated plastic hinge model; see the modeling diagram for details. Figure 4; Among them, the plastic hinge is simulated by a zero-length rotation spring. The specific derivation process is as follows: Since 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 : (4) (5) (6) in, is the transformation matrix, is the transposed matrix of the transformation matrix, To convert the angle.

[0026] Unit force increment vector in the global coordinate system : (7) (8) in, Respectively indicate the effect on Figure 4 (d) The force increments at nodes 1 and 3 are: is the force increment vector in the local coordinate system.

[0027] Unit displacement increment vector in the global coordinate system : (9) (10) in, Respectively indicate the effect on Figure 4 (d) The displacement increments of nodes 1 and 3, is the displacement increment vector of the local coordinate system; The matrix relationship in the overall coordinate system is sorted out: (11).

[0028] In the cantilever column concentrated plastic hinge model, the fixed end nodes of the zero-length rotation spring unit and the elastic beam-column unit connected to the ground represent the same point; therefore, the point cannot undergo displacement changes, that is, the boundary conditions must be met: , so formula (11) can be simplified to: (12) Respectively Figure 4 (d) The displacement increment of node 1, Respectively Figure 4(d) Force increment at node 1; Take the shear force increment in equation (12) and horizontal displacement increment Equality relationship, we get the equation: (13) Lateral stiffness of cantilever column: (14) The combined equations (2), (13) and (14) are simplified to obtain the rotation spring stiffness: (3) in, express Figure 4 (d) The horizontal displacement increment of node 1, express Figure 4 (d) The shear force increment at node 1; Expressed as the lateral stiffness of the column.

[0029] The state update algorithm of the new RC column concentrated plastic hinge model based on displacement loading control in Step 3 specifically refers to that the known displacement increment is applied to the corresponding degree of freedom and kept constant in each iteration step, and the spring rotation stiffness and stiffness matrix are updated based on equations (3) and (6), and the load increment factor is obtained accordingly. ; Load increment factor is a variable calculated during the equilibrium iterations through the load factor Determine the external load vector. For detailed steps, see Figure 2 .

[0030] The model verification and comparative analysis of Step 4 and Step 5 are based on the quasi-static loading test data of circular cross-section RC cantilever columns from the official website of PEER Structural Performance Database, which are the test data of bending failure, shear failure and bending-shear failure columns, and are referred to as column 1, column 2 and column 3 respectively; the horizontal displacement in the test data is brought into the state update algorithm of the new RC column concentrated plastic hinge model based on displacement loading control to obtain the corresponding base shear force, and the simulation results of this paper are compared with the simulation results of the existing model. This numerical experiment is divided into 4 working conditions: (1) The elastic beam-column element stiffness and the spring rotation stiffness are not corrected by the multiplier “n” (referred to as “existing model uncorrected”); (2) The multiplier “n” is set to 10 (referred to as “existing model n=10”); (3) The multiplier “n” is set to 100 (referred to as “existing model n = 100”); (4) Use the new method proposed in this paper to conduct modeling analysis (referred to as “this paper’s model”); Comparison of 4 working conditions , MAE, RMSE, Figure 5 , Figure 6 , Figure 7 The comparison chart of the simulation results of the existing model and the model in this paper with the experimental data is shown; the specific results are shown in Table 1: Table 1 Evaluation indexes of the simulation columns of the existing models and the proposed model

[0031] Table 1 shows in more detail the performance indicators of the existing concentrated plastic hinge model when the rotational stiffness of the elastic rod and the rotational stiffness of the spring are appropriately corrected. In Table 1, when n is 10 and n is 100, the simulation results are consistent 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), when n is 10 and n is 100, the The results are higher than those of the uncorrected multiplier "n" condition (i.e., the existing model is not corrected), and the MAE and RMSE are lower than those of the existing model. In addition, when n is 100, the simulation accuracy of the existing model is higher than that when n is 10, which is consistent with the previous discussion. For the same group of bending failure columns, shear failure columns, and bending-shear failure columns mentioned above, the column hysteresis curves simulated by the new model proposed in this paper are highly consistent with the corresponding test data. Moreover, by comparing the results obtained with the existing model, it can be seen that the new model proposed in this paper is The three simulation accuracy evaluation indicators of MAE and RMSE are better than the existing models, which further verifies the accuracy and reliability of the model in this paper.

[0032] In the preferred embodiment, the state update algorithm in Step 3 obtains the load increment factor by maintaining a constant displacement increment in each iteration step and updating the spring rotation stiffness and stiffness matrix using the functional relationship in Step 2. , and determine the external load vector through the load factor; the above settings ensure the stability and convergence of the algorithm, while improving the calculation efficiency; during the iteration process, the convergence criterion is dynamically adjusted to accurately control the balance between calculation accuracy and resource consumption.

[0033] In the preferred solution, the test data in Step 4 is derived from the quasi-static loading test data of a circular cross-section RC cantilever column of a certain official website, and the accuracy evaluation index of the simulation result adopts the determination coefficient , mean absolute error MAE and root mean square error RMSE; the above settings ensure a high degree of consistency between the simulation process and the actual test data. The prediction ability of the model is evaluated, and the MAE and RMSE quantify the error range, providing solid data support for structural safety assessment.

[0034] In the preferred scheme, the existing model in the Step 5 is compared and analyzed with the model in this paper. By taking different values ​​of the multiplier n, namely no correction, 10, and 100, the simulation accuracy is compared with the model in this paper, and it is verified that the model in this paper can achieve higher simulation accuracy without defining the multiplier n; the above settings, under the same experimental conditions, not only reduce the complexity of parameter settings, but also significantly improve the accuracy of prediction, proving the advantages of the model in this paper in improving simulation accuracy and simplifying model complexity.

[0035] In summary, the novel RC column concentrated plastic hinge model research method based on lateral stiffness provided by the present invention 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 lateral stiffness of the actual column and the rotational stiffness of the spring. The reliability and accuracy of the novel RC column concentrated plastic hinge model research method based on lateral stiffness are verified by comparative analysis of existing models, which has important practical significance for establishing an accurate and reasonable RC column nonlinear analysis model. The present invention proposes for the first time a novel RC column concentrated plastic hinge model research method based on lateral stiffness, which is completely different from the previous method that relies on the multiplier "n" to adjust the rotational spring stiffness and the elastic beam-column unit stiffness. The new method establishes a more direct and accurate simulation method by directly associating the rotational stiffness of the spring with the lateral stiffness of the component. The present invention derives the unit stiffness matrix of the cantilever column concentrated plastic hinge series model through mechanical relationships and geometric analysis, and establishes the The specific functional relationship between the rotational stiffness of the zero-length rotation spring and the lateral stiffness of the component, this derivation method starting from basic mechanics, makes the new model more rigorous and novel in theory; the scheme of the present invention proposes a new state update algorithm for the concentrated plastic hinge model of RC columns based on displacement loading control, and the algorithm updates the spring rotational stiffness and stiffness matrix in real time according to the displacement increment during the iteration process, thereby ensuring that the model can accurately simulate the nonlinear behavior of RC columns under different loading conditions; the successful proposal of this scheme not only provides new ideas and methods for the construction of nonlinear analysis models of RC columns, but also makes important contributions to the technological progress in the field of structural seismic design; through in-depth research and analysis, this scheme provides a useful reference and reference for the development and optimization of similar models in the future; at the same time, the application prospects of this research result are broad, and it is 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 new RC column concentrated plastic hinge model research method based on lateral stiffness, characterized by: The method comprises the following steps: Step 1: Derive the unit stiffness matrix of the cantilever column concentrated plastic hinge series model; Step 2: Based on the derived element stiffness matrix, establish the functional relationship between the rotational stiffness of the zero-length rotation spring and the lateral stiffness of the component; Step 3: A new state updating algorithm for concentrated plastic hinge model of RC columns based on displacement loading control; Step 4: Collect the test data of the existing test columns, and construct the new RC column concentrated plastic hinge model based on the state update algorithm to simulate the hysteresis curve of the column, obtain the accuracy evaluation index of the simulation results, and verify the accuracy of the model in this paper; Step 5: Use the existing concentrated plastic hinge model to simulate the hysteresis curve of the column. The simulation accuracy is controlled by the multiplier n. Compare the simulation accuracy of the existing model and the model proposed in this paper.

2. The research method of the new concentrated plastic hinge model of RC column based on lateral stiffness according to claim 1 is characterized in that: The theoretical basis for deriving the unit stiffness matrix in step 1 is to derive the unit stiffness matrix of the cantilever column concentrated plastic hinge series model based on the mechanical relationship and geometric analysis of the cantilever column unit with rigid nodes at both ends and the cantilever column unit with zero-length rotation spring at one end. , as follows: （1） Among them, E, I, A, and L represent the elastic modulus, moment of inertia, cross-sectional area, and rod length of the cantilever column, respectively; is the rotational stiffness of the spring; , are custom parameters, and their definitions are as follows: （2）。 3. The research method of the new concentrated plastic hinge model of RC column based on lateral stiffness according to claim 2 is characterized in that: The theoretical basis for the functional relationship between the rotational stiffness of the rotation spring and the lateral stiffness of the component in Step 2 is to establish the rotational stiffness of the spring through the mechanical relationship and geometric boundary conditions of the model based on the unit stiffness matrix of the cantilever column concentrated plastic hinge model derived in the previous article. The lateral stiffness of the member , free end angle increment , horizontal displacement increment The specific functional relationship of is as follows: （3）。 4. The research method of a new concentrated plastic hinge model of RC columns based on lateral stiffness according to claim 3 is characterized by: The state update algorithm in Step 3 obtains the load increment factor by maintaining a constant displacement increment in each iteration step and updating the spring rotation stiffness and stiffness matrix using the functional relationship in Step 2. , and determine the external load vector through the load factor.

5. The research method of a new concentrated plastic hinge model of RC columns based on lateral stiffness according to claim 4 is characterized by: The test data in Step 4 is derived from the quasi-static loading test data of circular cross-section RC cantilever columns. The accuracy evaluation index of the simulation results adopts the determination coefficient , mean absolute error MAE and root mean square error RMSE.

6. The new RC column concentrated plastic hinge model research method based on lateral stiffness according to claim 5 is characterized by: The existing model in Step 5 is compared and analyzed with the model in this paper. By taking different values ​​of the multiplier n, namely no correction, 10, and 100, the simulation accuracy is compared with the model in this paper, verifying that the model in this paper can achieve higher simulation accuracy without defining the multiplier n.

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