A simplified model analysis and simulation method considering in-plane and out-of-plane interaction of different stage infilled walls

Abstract

The application discloses a simplified model analysis simulation method considering in-plane and out-of-plane interaction of different stage infilled walls, and the method comprises the following steps: 1, determining the nodes of peripheral vertical and horizontal structural members, the end points and intermediate nodes of elastic-plastic bracing rods in the infilled wall, and the local nodes of horizontal structural members; 2, constructing an infilled wall simplified model; 3, performing fiber discretization on the elastic-plastic bracing rods in the infilled wall, and analyzing the in-plane and out-of-plane coupled seismic response of the infilled wall; 4, dividing different damage states of the infilled wall, and proposing the interaction relationship between the in-plane and out-of-plane of the infilled wall under different damage states; and 5, calculating the interaction curves of the infilled wall under different damage states. The application solves the pain point that the fiber area, distance and other parameters in the simplified model are difficult to dynamically adapt to different damage states, ensures that the mechanical parameters and the damage state are matched synchronously in the simulation process, and improves the result accuracy.

Description

Technical Field

[0001] This invention belongs to the field of seismic construction of buildings and relates to a simplified analysis and simulation method for infill walls. Specifically, it relates to a simplified model analysis and simulation method that considers the interaction between the infill walls inside and outside the plane at different stages. Background Technology

[0002] In the field of building structures, infill walls, as important non-structural components in frame structures, have always been a hot research topic due to their load-bearing performance and interaction with the main structure. Especially under complex loads, the coupling relationship between out-of-plane and in-plane loads on infill walls, and the resulting deterministic interaction mechanism between in-plane and out-of-plane displacements, are crucial for accurately assessing the safety and stability of structures under extreme seismic conditions. Currently, although some scholars have begun to focus on and engage in this research area, conducting preliminary discussions on the interaction between in-plane and out-of-plane displacement limits of rigidly connected infill walls under specific damage states, most of these studies are limited to specific damage states, load types, or boundary conditions, lacking research on the in-plane and out-of-plane interaction relationships of infill walls with different degrees of damage. Summary of the Invention

[0003] To address the problem that existing simulation methods cannot accurately account for the coupling of seismic performance between the in-plane and out-of-plane areas of infill walls, this invention provides a simplified model analysis and simulation method that considers the interaction between the in-plane and out-of-plane areas of infill walls at different stages, applicable to the analysis of the coupled seismic response between the in-plane and out-of-plane areas of infill walls.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A simplified model analysis and simulation method considering the in-plane and out-of-plane interactions of infill walls at different stages includes the following steps:

[0006] Step 1: Determine nodes 1, 2, 3, and 4 of the surrounding vertical and horizontal structural members; divide the elasto-plastic strut in the middle of the infill wall into two elasto-plastic struts with out-of-plane degrees of freedom bound to the intermediate nodes, and determine the four endpoints and two intermediate nodes of the elasto-plastic strut in the middle of the infill wall: endpoint 5, endpoint 6, endpoint 7, endpoint 8, intermediate node 9, and intermediate node 10; determine the local nodes 24, 25, 26, and 27 of the horizontal structural members;

[0007] Step 2: Connect node 1 and node 2 to form structural member 11; connect node 3 and node 4 to form structural member 13; connect node 2 and node 3 to form structural member 12; connect endpoint 5, intermediate node 9, and endpoint 8 to form the intermediate elastic-plastic strut 22 of the infill wall; connect endpoint 7, intermediate node 10, and endpoint 6 to form the intermediate elastic-plastic strut 23 of the infill wall; connect node 2 and endpoint 5 to form the rigid strut 14 of the infill wall; connect endpoint 5 and local node 25 to form the rigid strut 15 of the infill wall; connect node 4 and endpoint 8 to form the rigid strut of the infill wall. Stiffener 16 connects local node 26 and endpoint 8 to form rigid stiffener 17 for the infill wall; local node 24 connects local node 24 and endpoint 6 to form rigid stiffener 18 for the infill wall; node 3 connects node 3 and endpoint 6 to form rigid stiffener 19 for the infill wall; node 1 connects node 1 and endpoint 7 to form rigid stiffener 20 for the infill wall; and local node 27 connects local node 27 and endpoint 7 to form rigid stiffener 21 for the infill wall, thus obtaining a simplified model of the infill wall. Section and material properties are assigned to structural members 11, 12, and 13, and boundary conditions, mass, and loads are assigned to the simplified model of the infill wall.

[0008] Step 3: Discretize the fibers of the elastoplastic struts in the middle of the infill wall. Each fiber represents a small area on the cross section with different positions, cross-sectional areas and material properties. Analyze the coupled seismic response of the infill wall inside and outside the plane.

[0009] Step 4: Classify the infill wall into different damage states and propose the interaction relationship between the infill wall inside and outside the plane under different damage states;

[0010] Step 5: Calculate the interaction curves of the infill wall under three different damage states.

[0011] Compared with the prior art, the present invention has the following advantages:

[0012] 1. This invention covers the interaction study of different damage stages: It overcomes the shortcomings of existing technologies that are limited to specific damage states. By establishing the interaction relationship between the bearing capacity inside and outside the plane under each of the three clearly defined damage states of slight, moderate and severe (yield, peak and residual), it reflects the changes in mechanical behavior during the damage evolution process of the infill wall.

[0013] 2. In this invention, the strut is under compression regardless of whether the force is applied from left to right or from right to left, which better reflects the actual compression state of the infill wall under earthquake action.

[0014] 3. This invention achieves unified and accurate simulation of in-plane and out-of-plane forces: Through the model design of "8 rigid struts + 2 elastic-plastic struts bound to out-of-plane degrees of freedom", the elastic-plastic struts can simultaneously bear axial pressure and bending deformation, matching the in-plane axial bearing capacity, and through equivalent mass (81% of the self-weight of the infill wall) and bending bearing capacity calibration, ensuring that the out-of-plane mechanical properties are consistent with reality, thus solving the problem that existing models cannot take into account the two-way load coupling.

[0015] 4. Overcoming the challenge of dynamic parameter adjustment: The innovative method of "approximating different curvature curves with the same slope broken line" solves the problem that parameters such as fiber area and distance in the simplified model are difficult to dynamically adapt to different damage states (curvature changes), ensuring that mechanical parameters and damage states are synchronously matched during the simulation process and improving the accuracy of the results. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the infill wall and the intermediate elastic-plastic strut;

[0017] Figure 2 This is a schematic diagram of fiber discreteness;

[0018] Figure 3 Simplified in-plane load-displacement curve for infill walls;

[0019] Figure 4 Assignment diagram of interaction relationship curves;

[0020] Figure 5 These are the in-plane and out-of-plane interaction curves under different damage states. Detailed Implementation

[0021] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0022] This invention provides a simplified model analysis and simulation method for infill walls that consider in-plane and out-of-plane interactions at different stages. The method includes the following steps:

[0023] Step 1: Determine nodes 1, 2, 3, and 4 of the surrounding vertical and horizontal structural members; divide the elasto-plastic strut in the middle of the infill wall into two elasto-plastic struts with out-of-plane degrees of freedom bound to the intermediate nodes, and determine the four endpoints and two intermediate nodes of the elasto-plastic strut in the middle of the infill wall: endpoint 5, endpoint 6, endpoint 7, endpoint 8, intermediate node 9, and intermediate node 10. Among them, endpoint 5 and endpoint 7 are in the same position, endpoint 6 and endpoint 8 are in the same position, and intermediate node 9 and intermediate node 10 are in the same position; determine the local nodes 24, 25, 26, and 27 of the horizontal structural members.

[0024] In this step, the method for determining the positions of endpoints 5, 6, 7, 8, intermediate node 9, intermediate node 10, local node 24, local node 25, local node 26, and local node 27 is as follows: the angle between the line connecting node 2 and endpoint 5 and the line connecting node 2 and node 1 is 30-45 degrees; the angle between the line connecting node 1 and endpoint 7 and the line connecting node 1 and node 2 is 30-45 degrees; the angle between the line connecting node 3 and endpoint 6 and the line connecting node 3 and node 4 is 30-45 degrees; the angle between the line connecting node 4 and endpoint 8 and the line connecting node 4 and node 3 is 30-45 degrees; intermediate node 9 is set at the midpoint of the line connecting endpoint 5 and endpoint 8; intermediate node 10 is set at the midpoint of the line connecting endpoint 6 and endpoint 7; the distances between local nodes 24, 25, 26, and 27 and nodes 2, 3, 1, and 4 are respectively within 30% of the length of the horizontal structural member.

[0025] Step 2: Connect node 1 and node 2 to form structural member 11; connect node 3 and node 4 to form structural member 13; connect node 2 and node 3 to form structural member 12; connect endpoint 5, intermediate node 9, and endpoint 8 to form intermediate elastic-plastic strut 22 of the infill wall; connect endpoint 7, intermediate node 10, and endpoint 6 to form intermediate elastic-plastic strut 23 of the infill wall; connect node 2 and endpoint 5 to form rigid strut 14 of the infill wall; connect endpoint 5 and local node 25 to form rigid strut 15 of the infill wall; connect node 4 and endpoint 8 to form rigid strut 16 of the infill wall; connect local node 26 and endpoint 8 to form rigid strut 17 of the infill wall; connect local node 24 and endpoint 6 to form rigid strut 18 of the infill wall; connect node 3 and endpoint 6 to form rigid strut 19 of the infill wall; connect node 1 and endpoint 7 to form rigid strut 20 of the infill wall; connect local node 27 and endpoint 7 to form rigid strut 21 of the infill wall, thus obtaining a simplified model of the infill wall. Assign cross-sections and material properties to structural members 11, 12, and 13, and assign boundary conditions, mass, and loads to the model.

[0026] In this step, the simplified model of the infill wall consists of 8 rigid infill wall struts and 2 intermediate elastic-plastic struts. One node of each of the 8 rigid infill wall struts is a structural member node, and the other node connects to the end point of the intermediate elastic-plastic strut. The intermediate elastic-plastic strut is divided into two elastic-plastic struts that bind the out-of-plane degrees of freedom of the intermediate node, as shown below. Figure 1 As shown in the figure. Among them, the elastic-plastic strut in the middle of the infill wall can not only withstand axial pressure, but also simulate bending deformation, so as to realize a unified description of the in-plane and out-of-plane effects of the infill wall, thereby more accurately simulating the nonlinear stress behavior of the infill wall.

[0027] Step 3: Discretize the fibers of the elasto-plastic struts in the middle of the infill wall. Each fiber represents a small area on the cross section with different positions, cross-sectional areas and material properties. Analyze the coupled seismic response of the infill wall inside and outside the plane.

[0028] In this step, such as Figure 2 As shown, the method for fiber discretization of the elasto-plastic struts in the middle of the infill wall is as follows:

[0029] like Figure 1 As shown, when the infill wall is subjected to an in-plane load from left to right, the rigid struts of the blue infill wall are under compression, while the rigid struts of the red infill wall are not under load. In this case, the beam-column elements at the center are under compression. Conversely, when the infill wall is subjected to an in-plane load from right to left, the rigid struts of the red infill wall are under compression, and the beam-column elements at the center are still under compression, thus simulating the compression state of the infill wall under seismic loading. To ensure that the simplified model accurately reflects the mechanical properties of the infill wall under purely in-plane loads, the in-plane force-displacement relationship of the infill wall needs to be simplified, and the axial force-displacement relationship of the elasto-plastic struts in the middle of the infill wall needs to be determined through geometric transformation.

[0030] Calculate the in-plane bearing capacity of the simplified model of the infill wall :

[0031] (1)

[0032] (2)

[0033] (3)

[0034] In the formula: In-plane bearing capacity; For horizontal shearing capacity; This refers to the area of ​​the masonry infill. This refers to the thickness of the infill wall; This is the length of the infill wall; For the shear strength of the masonry; The expected weight of the wall panel.

[0035] The out-of-plane stress characteristics of the infill wall are reflected by the out-of-plane bending of the elasto-plastic strut in the middle of the infill wall. When an out-of-plane force is applied at the central node, the elasto-plastic strut in the middle of the infill wall becomes particularly important, as it determines the bending stiffness and failure mode of the wall. To accurately depict the mechanical behavior of the infill wall under purely out-of-plane loads, it is crucial to ensure that the maximum out-of-plane bending capacity of the elasto-plastic strut in the middle of the infill wall matches the actual out-of-plane load capacity of the infill wall. Simultaneously, under this condition, the deflection at the center point of the elasto-plastic strut in the middle of the infill wall should also be consistent with the out-of-plane displacement at the center point of the infill wall. Given that the simplified model of the infill wall can be considered as a simply supported beam with concentrated mass at mid-span in the out-of-plane direction, while the actual infill wall system behaves as a simply supported beam with distributed mass, to achieve the equality of their first-order natural frequencies, the equivalent mass of the infill wall at the central node of the simplified model is adjusted to 81% of the infill wall's self-weight.

[0036] Determine the out-of-plane bending capacity of the elastoplastic struts in the middle of the infill wall:

[0037] In this case, the relationship between the out-of-plane flexural capacity of the simplified model of the infill wall and the out-of-plane flexural capacity of the infill wall is as follows:

[0038] (4)

[0039] (5)

[0040] (6)

[0041] In the formula, The out-of-plane flexural capacity of the infill wall is simplified in the model. To simplify the model length for infill walls; This refers to the out-of-plane flexural capacity of the infill wall. This refers to the height of the infill wall; For out-of-plane uniformly distributed loads on the infill wall; The compressive strength of the masonry; Take 0.04.

[0042] Determine the moment of inertia of the cross section of the elastoplastic strut in the middle of the infill wall:

[0043] Based on the relationship between the deflection at the center point of the simplified infill wall model (i.e., the bending deformation of the simplified infill wall model) and the secant stiffness corresponding to the out-of-plane bearing capacity of the infill wall, the relationship between the out-of-plane moment of inertia and the secant stiffness of the simplified infill wall model can be established:

[0044] (7)

[0045] (8)

[0046] (9)

[0047] (10)

[0048] (11)

[0049] (12)

[0050] (13)

[0051] In the formula, Let be the moment of inertia of the cross section of the elasto-plastic strut in the middle of the infill wall; The secant stiffness is the out-of-plane bearing capacity of the infill wall. The elastic modulus of the infill wall; Out-of-plane effective weight; This represents the total weight of the infill wall. For heavy-duty infill walls; This is the first-order vibration frequency of the infill wall; It is the acceleration due to gravity; The moment of inertia of the infill wall section in its initial cracked state; This refers to the weight per unit length of the infill wall.

[0052] To simulate the in-plane and out-of-plane interaction of an infill wall under bidirectional loads, the cross-section of the elasto-plastic strut in the simplified model of the infill wall was meticulously designed. In the out-of-plane direction, the cross-section of the elasto-plastic strut was discretized into n fibers, each fiber representing a specific small region on the cross-section, with different locations, cross-sectional areas, and material properties. This design allows the invention to more accurately capture and describe the mechanical response of the infill wall under complex load conditions. Under the combined action of in-plane and out-of-plane loads, the plastic neutral axis of the elasto-plastic strut cross-section dynamically changes, particularly in the out-of-plane direction. This directly leads to corresponding changes in its in-plane axial bearing capacity and out-of-plane flexural bearing capacity. This change is a direct manifestation of the in-plane and out-of-plane interaction of the infill wall. As the axial force on the elasto-plastic strut cross-section gradually increases, the neutral axis tends to move towards the compressed side. This movement further affects the stress distribution of each fiber, potentially leading to a decrease in the overall flexural bearing capacity of the cross-section. Similarly, changes in the bending moment on the cross-section of the elasto-plastic strut in the middle of the infill wall also significantly affect the stress-strain state of each fiber. This process of mutual influence and dynamic adjustment allows the present invention to more comprehensively understand and predict the overall mechanical properties of the infill wall under complex loading conditions. In summary, by discretizing the cross-section of the elasto-plastic strut in the middle of the infill wall and considering the combined effects of in-plane and out-of-plane loads, the in-plane and out-of-plane interactions of the infill wall can be simulated more accurately, providing strong support for structural design and analysis.

[0053] Determine the fiber parameters after discretizing the cross-section of the elasto-plastic strut in the middle of the infill wall:

[0054] The in-plane axial bearing capacity of the infill wall under in-plane and out-of-plane loads out-of-plane flexural capacity The interaction curve between the fibers can determine the position and peak load capacity of each fiber. The calculation formula is as follows:

[0055] (14)

[0056] (15)

[0057] In the formula, For a discrete point sequence, when When =1, - The out-of-plane bending moment on the interaction curve is 0; For the first Peak load-bearing capacity of root fibers; for - The first interaction curve The in-plane axial bearing capacity at each discrete point; For the first The distance between the root fiber and the center of the wall section in the out-of-plane direction; for - The first interaction curve Out-of-plane flexural capacity at discrete points.

[0058] Therefore, the peak stress and peak strain of each fiber can be calculated according to equations (16) and (17):

[0059] (16)

[0060] (17)

[0061] In the formula, For the first Peak stress of the root fiber; For the first The area of ​​the root fiber; For the first Peak strain of the root fiber.

[0062] The cross-sectional area of ​​the discretized fibers needs to meet the following requirements: 1) The sum of the areas of all fibers is consistent with the cross-sectional area of ​​the elasto-plastic strut in the middle of the infill wall; 2) The moment of inertia of the discretized fiber cross-section is the same as that of the elasto-plastic strut in the middle of the infill wall. The cross-sectional area of ​​each fiber can be obtained by simultaneously solving the following equations:

[0063] (18)

[0064] (19)

[0065] In the formula, for The number of fibers on one side of the axis; The thickness of the infill wall; This refers to the width of the elastic-plastic strut in the middle of the infill wall.

[0066] Step 4: The infill wall exhibits different behaviors under different damage states. This step categorizes the infill wall into different damage states and proposes the in-plane and out-of-plane interaction relationships under these different damage states.

[0067] The in-plane and out-of-plane interactions of an infill wall exhibit significant differences as it undergoes different damage states. When the infill wall is slightly damaged, the influence of in-plane forces on out-of-plane deformation is not significant, and the interaction between the two is weak. Out-of-plane deformation is more controlled by its own out-of-plane loads and boundary conditions. However, as the damage gradually worsens, when the infill wall enters a moderately damaged state, the stress redistribution within the wall caused by in-plane forces begins to significantly affect the out-of-plane mechanical behavior. In-plane and out-of-plane deformations become coupled to some extent, and the interaction gradually strengthens. When the infill wall reaches a severely damaged state or is even on the verge of collapse, the in-plane and out-of-plane interactions become highly complex. The propagation of in-plane cracks and nonlinear deformation of the material greatly alter the out-of-plane load-bearing and deformation characteristics. The mechanical responses inside and outside the plane are closely intertwined, and the interaction relationship has fundamentally changed compared to the slightly damaged state.

[0068] From the perspective of damage development patterns and mechanical properties of infill walls, there is a close and specific correspondence between different damage states and load-bearing capacity states. Typically, when an infill wall is in a state of slight damage, its in-plane and out-of-plane strength has reached the yield level. This means that at this damage stage, the infill wall's performance in terms of axial force in the in-plane and flexural force in the out-of-plane begins to change significantly. In other words, the load-bearing capacity and deformation capacity exhibited by the infill wall in the state of slight damage are similar to, and equivalent to, the mechanical properties exhibited in the yield state. When the infill wall further develops to a state of moderate damage, its in-plane and out-of-plane strengths reach their peak values. This stage signifies that the infill wall has reached its performance limit in resisting loads, and its load-bearing capacity has reached its maximum. The peak value corresponding to the state of severe damage clearly defines the load-bearing limit of the infill wall within the normal stress range, providing a crucial basis for subsequent failure assessment. Furthermore, there is a direct correspondence between the failure state and the collapse state of the infill wall. The collapse state is the final failure form of the infill wall under load, representing that the structure has completely lost its load-bearing capacity and stability. When the infill wall reaches a state of collapse, it means that it has entered a state of failure.

[0069] Therefore, the interaction between the in-plane axial bearing capacity and the out-of-plane flexural bearing capacity of the simplified model of the infill wall can be expressed as follows:

[0070] yield:

[0071] (20)

[0072] Peak value:

[0073] (twenty one)

[0074] Residue:

[0075] (twenty two)

[0076] In the formula, The in-plane axial bearing capacity of the simplified model of the infill wall in its current state; Out-of-plane flexural capacity of the simplified model of the infill wall under the current condition; The in-plane yield point bearing capacity of a simplified model of an infill wall under pure in-plane load; The out-of-plane yield point flexural bearing capacity of a simplified model of an infill wall under pure out-of-plane load; The in-plane peak bearing capacity of a simplified model of an infill wall under pure in-plane load; The out-of-plane peak flexural capacity of a simplified model of an infill wall under pure out-of-plane load. The in-plane residual point bearing capacity of a simplified model of an infill wall under pure in-plane load; The out-of-plane residual bending capacity of the infill wall under a simplified model of pure out-of-plane load.

[0077] The in-plane forces on the infill wall can be simplified to the compression of an equivalent strut. To calibrate this equivalent strut, the simplified in-plane load-displacement curve of the infill wall is first needed, such as... Figure 3 As shown. In the simplified in-plane load-displacement curve, the in-plane stress behavior of the infill wall can be described by the following three characteristic points:

[0078] (1) Yield point: indicates that the infill wall begins to yield and its stiffness changes;

[0079] (2) Peak point: represents the maximum bearing capacity of the infill wall under in-plane load;

[0080] (3) Failure point: indicates the final failure of the infill wall.

[0081] By determining the yield point, peak point, and failure point, a simplified load-displacement curve of the equivalent diagonal strut of the infill wall is constructed. This allows for the further construction of the stress-strain relationship of each fiber beam element in the equivalent diagonal strut of the infill wall, enabling the simplified model to accurately simulate the in-plane stress performance of the infill wall.

[0082] The relationship between yield strength and corresponding in-plane displacement can be expressed as follows:

[0083] (twenty three)

[0084] (twenty four)

[0085] The relationship between peak intensity and corresponding in-plane displacement can be expressed as follows:

[0086] (25)

[0087] (26)

[0088] The relationship between residual strength and corresponding in-plane displacement can be expressed as follows:

[0089] = 0.85 (27)

[0090] (28)

[0091] In the formula, Yield strength; Peak intensity; Residual strength; This represents the in-plane displacement corresponding to the yield strength. This represents the in-plane displacement corresponding to the peak intensity. This represents the in-plane displacement corresponding to the residual strength. For axial stiffness; The stiffness of the reinforced segment of the equivalent strut load-displacement curve for the infill wall; The angle between the infill wall struts.

[0092] Step 5: Calculate the interaction curves of the infill wall under three different damage states.

[0093] In the analysis of the simplified model of infill walls, a tricky problem arises when dealing with variations in curvature. These three curves each have a unique distribution of load-bearing capacity or bending moment, and their allocated areas and fiber cross-section distances change with curvature. However, in the established simplified model, the key parameters such as the area and distance of the fiber cross-section elements are determined at the start of the simulation. During the simulation, it is difficult to dynamically change the area and distance of these fibers, making it difficult to accurately simulate the actual mechanical behavior of the structure under different curvature variations, i.e., different damage states, thus affecting the accuracy of the simulation results. Essentially, it's the reciprocal of the slope of the secant line in the PM interaction curve. This means the problem can be transformed into how to approximate the curve using a secant line. Specifically, it involves using a series of broken lines with the same slope to represent curves with different curvatures, in order to achieve a more reasonable simulation of mechanical properties in a simplified model.

[0094] Therefore, to address the above problems, this invention proposes an effective solution, the specific process of which is as follows:

[0095] Step 1: Segment the yield curve and calculate the slope of the broken line. First, select the curve with the largest curvature from the three curves in equations (20), (21), and (22), which is the curve corresponding to the yield state of the structure, i.e., equation (20). In the first quadrant, divide the curve evenly into segments according to the specified angle. part, Take an odd number, and the angle of each segment is... .by As the x-axis, y is the vertical axis, where For in-plane loads, For in-plane peak load, The out-of-plane bending moment, This represents the maximum out-of-plane bending moment. The result is obtained by calculating the slope of each segment of the broken line. slope of the broken line ( =1,2,⋯), such as Figure 4 As shown.

[0096] (29)

[0097] Step 2: Determine the segmentation points of the other two curves based on the slope of the broken line of the yield curve. After obtaining the slope of the broken line of the yield curve... Then, these slopes are used to derive the curves step by step from both ends towards the middle. That is, while keeping the slopes constant, points on the other two curves are connected sequentially from both ends towards the middle to determine the segmentation points of the other two curves. This method ensures that all three curves have the same slope within their corresponding segmented intervals. Figure 5 As can be seen intuitively, the broken line obtained in this way can approximately represent three curves with different curvatures, while ensuring that their slopes are equal in corresponding segments.

[0098] Step 3: Calculate the actual load, bending moment, and distance. After determining the segmentation points and corresponding slopes of the three curves, multiply them by the load. and reference bending moment The actual load can then be obtained. and actual bending moment ( =1,2,...). With the actual load and bending moment values, we can further calculate parameters such as the fiber cross-sectional area allocated to the corresponding curve and the stress and strain of the structure at different locations.

[0099] Example:

[0100] This embodiment provides a single-story, single-span reinforced concrete frame with a story height of 1700mm, a span of 2300mm, an infill wall thickness of 100mm, a height of 1400mm, a width of 2100mm, and a length of 1045mm for the elastic-plastic strut in the middle of the infill wall.

[0101] Step 1: In the OpenSees finite element software, create the corresponding reinforced concrete frame model by defining geometric parameters, defining node coordinates, defining beam and column sections, defining beam and column elements, and defining loads.

[0102] Step 2: Simplify the in-plane bearing capacity of the infill wall model Perform calculations, where It is 0.23 MPa. Take 50kN.

[0103] Step 3: Calculate the out-of-plane bending capacity of the simplified model of the infill wall strut. The resultant force of the uniformly distributed out-of-plane load is 60kN. The out-of-plane bending capacity of the simplified model of the infill wall is thus obtained.

[0104] Step 4: Calculate the out-of-plane moment of inertia of the simplified infill wall model, where the elastic modulus is 1260 MPa. The calculated out-of-plane moment of inertia is 5887.47 cm. 4 .

[0105] Step 5: The curve was divided into 9 segments according to angles of 10 degrees, 20 degrees, 30 degrees, 40 degrees, 50 degrees, 60 degrees, 70 degrees, 80 degrees, and 90 degrees. As the x-axis, Using the vertical axis as the ordinate, the slope of each segment of the broken line is calculated to obtain... slope of the broken line ( =1,2,...,9). After determining the slope, multiply it by the load respectively. and reference bending moment The actual load can then be obtained. and actual bending moment ( =1,2,...,9). With the actual load and bending moment values, we can further calculate the fiber cross-sectional area allocated to the corresponding curve, the stress and strain of the structure at different locations, and other parameters, as shown in Tables 1-3.

[0106]

[0107]

[0108]

[0109] In summary, by using the above-mentioned method of approximating curves with different curvatures using broken lines with the same slope, the difficulty of dynamically changing the fiber area and distance in the simplified model can be overcome to a certain extent. This allows for a more accurate simulation of the mechanical properties of the structure under different curvature variations, providing strong support for the analysis and design of the simplified model of infill walls.

Claims

1. A simplified model analysis and simulation method considering the in-plane and out-of-plane interactions of infill walls at different stages, characterized in that... The method includes the following steps: Step 1: Determine nodes 1, 2, 3, and 4 for the surrounding vertical and horizontal structural members; divide the elasto-plastic strut in the middle of the infill wall into two elasto-plastic struts with out-of-plane degrees of freedom bound to the intermediate nodes, and determine the four endpoints and two intermediate nodes of the elasto-plastic strut in the middle of the infill wall: endpoint 5, endpoint 6, endpoint 7, endpoint 8, intermediate node 9, and intermediate node 10; determine the local nodes 24, 25, 26, and 27 for the horizontal structural members, and set the intermediate node 9 at the midpoint of the line connecting endpoints 5 and 8, and set the intermediate node 10 at the midpoint of the line connecting endpoints 6 and 7; the distances between local nodes 24, 25, 26, and 27 and nodes 2, 3, 1, and 4 respectively are within 30% of the length of the horizontal structural member; Step 2: Connect node 1 and node 2 to form structural member 11; connect node 3 and node 4 to form structural member 13; connect node 2 and node 3 to form structural member 12; connect endpoint 5, intermediate node 9, and endpoint 8 to form the intermediate elastic-plastic strut 22 of the infill wall; connect endpoint 7, intermediate node 10, and endpoint 6 to form the intermediate elastic-plastic strut 23 of the infill wall; connect node 2 and endpoint 5 to form the rigid strut 14 of the infill wall; connect endpoint 5 and local node 25 to form the rigid strut 15 of the infill wall; connect node 4 and endpoint 8 to form the rigid strut of the infill wall. Stiffener 16 connects local node 26 and endpoint 8 to form rigid stiffener 17 for the infill wall; local node 24 connects local node 24 and endpoint 6 to form rigid stiffener 18 for the infill wall; node 3 connects node 3 and endpoint 6 to form rigid stiffener 19 for the infill wall; node 1 connects node 1 and endpoint 7 to form rigid stiffener 20 for the infill wall; and local node 27 connects local node 27 and endpoint 7 to form rigid stiffener 21 for the infill wall, thus obtaining a simplified model of the infill wall. Section and material properties are assigned to structural members 11, 12, and 13, and boundary conditions, mass, and loads are assigned to the simplified model of the infill wall. Step 3: Discretize the fibers of the elastoplastic struts in the middle of the infill wall. Each fiber represents a small area on the cross section with different positions, cross-sectional areas and material properties. Analyze the coupled seismic response of the infill wall inside and outside the plane. Step 4: Classify the infill wall into different damage states and propose the interaction relationship between the infill wall inside and outside the plane under different damage states; Step 5: Calculate the interaction curves of the infill wall under three different damage states: yield, peak, and residual.

2. The simplified model analysis and simulation method for infill wall interaction at different stages, as described in claim 1, is characterized in that... In step one, the method for determining the positions of endpoints 5, 6, 7, 8, intermediate node 9, intermediate node 10, local node 24, local node 25, local node 26, and local node 27 is as follows: the angle between the line connecting node 2 and endpoint 5 and the line connecting node 2 and node 1 is 30-45 degrees; the angle between the line connecting node 1 and endpoint 7 and the line connecting node 1 and node 2 is 30-45 degrees; the angle between the line connecting node 3 and endpoint 6 and the line connecting node 3 and node 4 is 30-45 degrees; and the angle between the line connecting node 4 and endpoint 8 and the line connecting node 4 and node 3 is 30-45 degrees.

3. The simplified model analysis and simulation method for infill wall interaction at different stages, as described in claim 1, is characterized in that... In step three, the method for fiber discretization of the elastic-plastic struts in the middle of the infill wall is as follows: (1) Calculate the in-plane bearing capacity of the simplified model of the infill wall : In the formula: In-plane bearing capacity; For horizontal shearing capacity; This refers to the area of ​​the masonry infill. This refers to the thickness of the infill wall; This is the length of the infill wall; For the shear strength of the masonry; The expected weight of the wall panel; (2) Determine the out-of-plane bending capacity of the elastic-plastic struts in the middle of the infill wall: The relationship between the out-of-plane flexural capacity of the simplified model of the infill wall and the out-of-plane flexural capacity of the infill wall is shown below: In the formula, The out-of-plane flexural capacity of the infill wall is simplified in the model. To simplify the model length for infill walls; This refers to the out-of-plane flexural capacity of the infill wall. This refers to the height of the infill wall; (3) Determine the moment of inertia of the cross section of the elastic-plastic strut in the middle of the infill wall: Based on the relationship between the deflection at the center point of the simplified infill wall model (i.e., the bending deformation of the simplified infill wall model) and the secant stiffness corresponding to the out-of-plane bearing capacity of the infill wall, the relationship between the out-of-plane moment of inertia and the secant stiffness of the simplified infill wall model is established: In the formula, Let be the moment of inertia of the cross section of the elasto-plastic strut in the middle of the infill wall; The secant stiffness is the out-of-plane bearing capacity of the infill wall. The elastic modulus of the infill wall; (4) In the out-of-plane direction, the cross section of the elastic-plastic strut in the middle of the infill wall is discretized into n fibers, each fiber representing a specific small area on the cross section, and these areas have different positions, cross-sectional areas and material properties; (5) Determine the fiber parameters after discretization of the cross-section of the elasto-plastic strut in the middle of the infill wall: The in-plane axial bearing capacity of the infill wall under in-plane and out-of-plane loads out-of-plane flexural capacity The interaction curves between the fibers determine the location and peak intensity of each fiber, and the calculation formula is as follows: In the formula, For a discrete point sequence, when When =1, - The out-of-plane bending moment on the interaction curve is 0; For the first Peak load-bearing capacity of root fibers; for - The first interaction curve The in-plane axial bearing capacity at each discrete point; For the first The distance between the root fiber and the center of the wall section in the out-of-plane direction; for - The first interaction curve Out-of-plane flexural capacity at discrete points; Therefore, the peak stress and peak strain of each fiber are calculated according to the following formula: In the formula, For the first Peak stress of the root fiber; For the first The area of ​​the root fiber; For the first Peak strain of the root fiber; (6) By simultaneously solving the following equations, the cross-sectional area of ​​each fiber can be obtained: In the formula, for The number of fibers on one side of the axis; The thickness of the infill wall; This refers to the width of the elastic-plastic strut in the middle of the infill wall.

4. The simplified model analysis and simulation method for infill wall interaction at different stages, as described in claim 3, is characterized in that... In (2), the out-of-plane flexural bearing capacity of the infill wall The calculation formula is as follows: In the formula, For out-of-plane uniformly distributed loads on the infill wall; The compressive strength of the masonry; Take 0.

04.

5. The simplified model analysis and simulation method for infill wall interaction at different stages, as described in claim 3, is characterized in that... In (3), the secant stiffness corresponding to the out-of-plane bearing capacity of the infill wall The calculation formula is as follows: In the formula, This represents the total weight of the infill wall. For heavy-duty infill walls; This is the first-order vibration frequency of the infill wall; It is the acceleration due to gravity; The moment of inertia of the infill wall section in its initial cracked state; This refers to the weight per unit length of the infill wall.

6. The simplified model analysis and simulation method for considering the in-plane and out-of-plane interactions of infill walls at different stages, as described in claim 3, is characterized in that... In (6), the cross-sectional area of ​​the discrete fibers needs to meet the following requirements: 1) the sum of the areas of each fiber is consistent with the cross-sectional area of ​​the elastic-plastic strut in the middle of the infill wall; 2) the moment of inertia of the discrete fiber cross-section is the same as the moment of inertia of the elastic-plastic strut in the middle of the infill wall.

7. The simplified model analysis and simulation method for infill wall interaction at different stages, as described in claim 1, is characterized in that... In step four, the interaction relationship between the in-plane axial bearing capacity and the out-of-plane flexural bearing capacity of the simplified model of the infill wall is expressed as follows: yield: (1) Peak value: (2) Residue: (3) In the formula, The in-plane axial bearing capacity of the simplified model of the infill wall in its current state; Out-of-plane flexural capacity of the simplified model of the infill wall under the current condition; The in-plane yield point bearing capacity of a simplified model of an infill wall under pure in-plane load; The out-of-plane yield point flexural bearing capacity of a simplified model of an infill wall under pure out-of-plane load; The in-plane peak bearing capacity of a simplified model of an infill wall under pure in-plane load; The out-of-plane peak flexural capacity of a simplified model of an infill wall under pure out-of-plane load. The in-plane residual point bearing capacity of a simplified model of an infill wall under pure in-plane load; The out-of-plane residual bending capacity of a simplified model of an infill wall under pure out-of-plane load; The relationship between yield strength and corresponding in-plane displacement is expressed as follows: (4) (5) The relationship between peak intensity and corresponding in-plane displacement is expressed as follows: (6) (7) The relationship between residual strength and corresponding in-plane displacement is expressed as follows: = 0.85 (8) (9) In the formula, Yield strength; Peak intensity; Residual strength; This represents the in-plane displacement corresponding to the yield strength. This represents the in-plane displacement corresponding to the peak intensity. This represents the in-plane displacement corresponding to the residual strength. For axial stiffness; The stiffness of the reinforced segment of the equivalent strut load-displacement curve for the infill wall; For horizontal shearing capacity; The angle between the infill wall struts.

8. The simplified model analysis and simulation method for infill wall interaction at different stages, as described in claim 7, is characterized in that... The specific steps of step five are as follows: Step 1: Segment the yield curve and calculate the slope of the broken line: Select the curve with the largest curvature from the three curves in equations (1), (2), and (3), and divide the curve evenly into segments in the first quadrant according to the specified angle. part, Take an odd number, and the angle of each segment is... ;by As the x-axis, y is the vertical axis, where For in-plane loads, For in-plane peak load, The out-of-plane bending moment, To obtain the maximum out-of-plane bending moment, the slope of each segment of the broken line is calculated. slope of the broken line ; The second step is to determine the segmentation points of the other two curves based on the slope of the broken line of the yield curve: after obtaining the slope of the broken line of the yield curve... Then, these slopes are used to gradually derive from both ends of the curve toward the middle, that is, while keeping the slopes constant, the points on the other two curves are connected one after another from both ends toward the middle, so as to determine the segmentation points of the other two curves. Step 3: Calculate the actual load, bending moment, and distance: After determining the segmentation points and corresponding slopes of the three curves, multiply them by the load. and reference bending moment To obtain the actual load and actual bending moment Further calculations were performed on the fiber cross-sectional area assigned to the corresponding curve and the stress and strain of the structure at different locations.

9. The simplified model analysis and simulation method for infill wall interaction at different stages, as described in claim 8, is characterized in that... The .

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