Simplified analysis simulation method for nine-pole filling wall

Abstract

The application discloses a nine-brace filling wall simplified analysis simulation method, and comprises the following steps: step one, determining the nodes of the peripheral vertical and horizontal structural members, determining the two end points and the intermediate node of the intermediate elastic-plastic brace, additionally setting two nodes at the same position of the two end points, and determining the local nodes of the horizontal structural members; step two, constructing a filling wall nine-brace simplified model composed of eight filling wall rigid braces and the intermediate elastic-plastic brace of the filling wall; step three, performing fiber discretization on the intermediate elastic-plastic brace of the filling wall, each fiber representing a small area on a section, having different positions, section areas and material properties, and analyzing the in-plane and out-of-plane coupling seismic responses of the filling wall. The application is mainly used for analyzing the in-plane and out-of-plane seismic responses of the filling wall under the action of earthquakes, can better reflect the actual working state of the filling wall under the condition of ensuring the accuracy, and is convenient for engineering application.

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 an analysis method for the coupled seismic response of infill walls inside and outside the plane. Background Technology

[0002] Masonry infill wall reinforced concrete frame structure is one of the most widely used building structure forms. Masonry infill walls can be flexibly arranged, serving both as the external enclosure structure of a building and as a partition for internal spaces to meet the diverse functional needs of a building.

[0003] An equivalent strut simplifies the function of an infill wall by representing it as a strut-like component. It typically assumes the infill wall interacts with the main structure through some means (such as stiffness or strength), and by analyzing its mechanical properties, it is transformed into an equivalent strut. In frame structures, infill walls often exist as non-load-bearing walls, but in reality, they can affect the overall stability of the frame structure. By treating infill walls as equivalent struts, the stress state of the building can be predicted and analyzed more accurately. Under seismic loads, infill walls may affect the seismic response of the frame structure. The equivalent strut model allows for a more reasonable simulation of the infill wall's performance under seismic loads. This model significantly simplifies the analysis of the infill wall's function, improves the efficiency of design calculations, and helps ensure that the influence of infill walls is considered in structural analysis, thereby avoiding potential structural safety hazards.

[0004] As non-structural components, infill walls undergo in-plane and out-of-plane coupled failure modes during earthquakes. Therefore, a simplified model of infill walls that can reasonably and effectively reflect their in-plane and out-of-plane behavior, as well as the infill wall-frame collaborative working mechanism, is crucial for the accuracy and cost-effectiveness of the analysis results. The strut model is the most widely used simplified model for infill walls; however, most of these models can only simulate the in-plane mechanical properties of the infill wall. Simplified models that consider the coupling effect of the in-plane and out-of-plane mechanical properties of the infill wall are rare, and they cannot effectively predict the nonlinear behavior and out-of-plane collapse of the infill wall after cracking. Therefore, it is necessary to find a scientifically reasonable and accurate three-dimensional simplified analysis model that accurately reflects the wall-frame collaborative working mechanism to reveal the typical seismic damage and failure mechanisms of infill wall frame structures. Summary of the Invention

[0005] 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 analysis and simulation method for nine-strut infill walls.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A simplified analysis and simulation method for a nine-strut infill wall includes the following steps:

[0008] Step 1: Determine nodes 1, 2, 3, and 4 of the surrounding vertical and horizontal structural members; determine the two end points 5 and 6 of the intermediate elastic-plastic strut and the intermediate node 56; set nodes 51 and 52, and nodes 61 and 62 at the same position on end points 5 and 6 respectively; determine the local nodes 7, 8, 9, and 10 of the horizontal structural members.

[0009] Step 2: Connect node 1 and node 2 to form structural member 11; connect node 3 and node 4 to form structural member 12; connect node 2 and node 3 to form structural member 13; connect endpoint 5, node 56, and endpoint 6 to form the intermediate elastic-plastic strut 14 of the infill wall; connect node 2 and node 51 to form the rigid strut 15 of the infill wall; connect local node 8 and node 51 to form the rigid strut 16 of the infill wall; connect local node 7 and node 61 to form the rigid strut 17 of the infill wall; connect node 3 and node 61 to form the rigid strut 18 of the infill wall; connect node 1 and node 52 to form the rigid strut 19 of the infill wall; connect local node 10 and node 52 to form the rigid strut 20 of the infill wall. Connecting local nodes 9 and 62 forms rigid strut 21 for the infill wall; connecting nodes 4 and 62 forms rigid strut 22 for the infill wall; connecting nodes 51 and endpoint 5 forms zero-length element 23; connecting nodes 52 and endpoint 5 forms zero-length element 24; connecting nodes 61 and endpoint 6 forms zero-length element 25; connecting nodes 62 and endpoint 6 forms zero-length element 26, thus obtaining a simplified model of the nine struts for the infill wall; assigning section and material properties to structural members 11, 12, and 13; assigning material properties to zero-length elements 23, 24, 25, and 26; and assigning boundary conditions, mass, and loads to the simplified model of the nine struts for the infill wall.

[0010] 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.

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

[0012] 1. Compared with a single strut, the nine struts in this invention not only take into account the influence of the nodes, but also the influence on the frame beams and columns.

[0013] 2. Compared to the five-strut design, the nine-strut design in this invention is always 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 conditions.

[0014] 3. This invention is mainly used for analyzing the seismic response of infill walls inside and outside the plane under seismic action. Under the condition of ensuring accuracy, it can better reflect the actual working state of the infill wall and facilitate engineering applications. Attached Figure Description

[0015] Figure 1 A schematic diagram of a nine-strut infill wall and a schematic diagram of the intermediate elastic-plastic strut;

[0016] Figure 2 This is a schematic diagram of fiber discreteness;

[0017] Figure 3 This is a graph showing the interaction relationship between PM and PM.

[0018] Figure 4 This is a load-displacement curve in a plane.

[0019] Figure 5 This is an out-of-plane load-displacement curve. Detailed Implementation

[0020] 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.

[0021] This invention provides a simplified analysis and simulation method for a nine-strut infill wall, the method comprising the following steps:

[0022] Step 1: Determine nodes 1, 2, 3, and 4 of the surrounding vertical and horizontal structural members; determine the two end points 5 and 6 of the intermediate elastic-plastic strut and the intermediate node 56; set nodes 51 and 52, and nodes 61 and 62 at the same positions of end points 5 and 6 respectively; determine the local nodes 7, 8, 9, and 10 of the horizontal structural members.

[0023] In this step, the method for determining the positions of endpoints 5 and 6, as well as local nodes 7, 8, 9, and 10, 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 5 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 6 and the line connecting node 4 and node 3 is 30-45 degrees; the distances between local nodes 7, 8, 9, and 10 and nodes 2, 3, 1, and 4 are respectively within 30% of the length of the horizontal structural member; node 56 is set at the midpoint of the line connecting endpoints 5 and 6.

[0024] Step 2: Connect node 1 and node 2 to form structural member 11; connect node 3 and node 4 to form structural member 12; connect node 2 and node 3 to form structural member 13; connect endpoint 5, node 56, and endpoint 6 to form the intermediate elastic-plastic strut 14 of the infill wall; connect node 2 and node 51 to form the rigid strut 15 of the infill wall; connect local node 8 and node 51 to form the rigid strut 16 of the infill wall; connect local node 7 and node 61 to form the rigid strut 17 of the infill wall; connect node 3 and node 61 to form the rigid strut 18 of the infill wall. Connecting node 1 and node 52 forms rigid strut 19 for the infill wall; connecting local node 10 and node 52 forms rigid strut 20 for the infill wall; connecting local node 9 and node 62 forms rigid strut 21 for the infill wall; connecting node 4 and node 62 forms rigid strut 22 for the infill wall; connecting node 51 and endpoint 5 forms zero-length element 23; connecting node 52 and endpoint 5 forms zero-length element 24; connecting node 61 and endpoint 6 forms zero-length element 25; connecting node 62 and endpoint 6 forms zero-length element 26, resulting in a simplified model of the nine struts for the infill wall. Structural members 11, 12, and 13 are assigned section and material properties, and zero-length elements 23, 24, 25, and 26 are assigned material properties. Boundary conditions, mass, and loads are assigned to the model.

[0025] In this step, the simplified model of the nine-strut infill wall consists of eight rigid infill wall struts and an elastic-plastic strut in the middle of the infill wall. One node of each of the eight rigid infill wall struts is a node of a structural member, and the other node is connected to the elastic-plastic strut in the middle of the infill wall through a zero-length element. Figure 1 As shown, the elasto-plastic strut in the middle of the infill wall is divided into two elements connected by a central node. This strut can withstand axial compression and simulate bending deformation, providing a unified description of the in-plane and out-of-plane forces acting on the infill wall, thus more accurately simulating its nonlinear stress behavior. The model introduces four zero-length elements at both ends of the elasto-plastic strut to connect it to the rigid strut. Each zero-length element contains six degrees of freedom: infinite compressive strength and infinitesimal tensile strength in the horizontal direction within the plane; and infinite strength in the other five degrees of freedom.

[0026] 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.

[0027] 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:

[0028] like Figure 1As 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.

[0029] In-plane bearing capacity of a simplified model of a nine-strut infill wall The calculation method is as follows:

[0030] (1)

[0031] (2)

[0032] (3)

[0033] 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; This refers to the shear strength of the masonry.

[0034] The out-of-plane stress characteristics of the infill wall are reflected by the out-of-plane bending of the intermediate elasto-plastic strut. When an out-of-plane force is applied at the central node, the intermediate elasto-plastic strut and the zero-length element become particularly important, as they determine the wall's bending stiffness and failure mode. 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 intermediate elasto-plastic strut matches the actual out-of-plane load capacity of the infill wall. Simultaneously, under this condition, the deflection at the center point of the intermediate elasto-plastic strut should also be consistent with the out-of-plane displacement at the center point of the infill wall. Given that the simplified nine-strut model of the infill wall can be considered 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 equality of their first-order natural frequencies, the equivalent mass of the infill wall at the central node of the simplified nine-strut model is adjusted to 81% of the infill wall's self-weight.

[0035] Determine the out-of-plane bending capacity of the elastoplastic struts in the middle of the infill wall:

[0036] In this case, the relationship between the out-of-plane flexural capacity of the simplified nine-strut model of the infill wall and the out-of-plane flexural capacity of the infill wall is as follows:

[0037] (4)

[0038] (5)

[0039] (6)

[0040] In the formula, Out-of-plane bending capacity of a simplified model of a nine-strut infill wall; To simplify the model length for the nine struts used to fill the wall; 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.

[0041] Determine the moment of inertia of the cross section of the elastoplastic strut in the middle of the infill wall:

[0042] Based on the relationship between the deflection at the center point of the simplified nine-strut model of the infill wall (i.e., the bending deformation of the simplified nine-strut model of the infill wall) 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 nine-strut model of the infill wall can be established:

[0043] (7)

[0044] (8)

[0045] (9)

[0046] (10)

[0047] (11)

[0048] (12)

[0049] (13)

[0050] 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.

[0051] To simulate the in-plane and out-of-plane interaction of an infill wall under bidirectional loads, the cross-section of the intermediate elasto-plastic strut in the simplified nine-strut model of the infill wall was meticulously designed. In the out-of-plane direction, the cross-section of the intermediate 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 intermediate elasto-plastic strut cross-section undergoes dynamic 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 intermediate 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.

[0052] Determine the fiber parameters after discretizing the cross-section of the elasto-plastic strut in the middle of the infill wall:

[0053] like Figure 3 As shown, 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:

[0054] (14)

[0055] (15)

[0056] 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.

[0057] Therefore, the peak stress and peak strain of each fiber can be calculated according to equations (8) and (9):

[0058] (16)

[0059] (17)

[0060] 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.

[0061] 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:

[0062] (18)

[0063] (19)

[0064] 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.

[0065] Example:

[0066] This example 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.

[0067] 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.

[0068] Step 2: Simplify the in-plane bearing capacity of the nine-strut model of the infill wall. Perform calculations, where It is 0.23 MPa. Taking 50kN, the calculation is as follows It is 46.75 kN.

[0069] Step 3: Calculate the out-of-plane flexural capacity of the simplified model of the nine-strut infill wall. The resultant force of the uniformly distributed out-of-plane load is 60kN, i.e. The value is 10.5 kN·m, from which the out-of-plane bending capacity of the simplified model of the nine-strut infill wall is calculated to be 12.31 kN·m.

[0070] Step 4: Calculate the out-of-plane moment of inertia of the simplified model of the nine-strut infill wall, where the elastic modulus is 1260 MPa. The calculated out-of-plane moment of inertia is 5887.47 cm. 4 .

[0071] Step 5: In the out-of-plane direction, discretize the elasto-plastic strut cross-section into 10 fibers, each fiber representing a specific small region on the cross-section, with different locations, cross-sectional areas, and material properties. Measure 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 them can determine the position of each fiber. The peak intensity σ is shown in Tables 1 and 2.

[0072]

[0073]

[0074] Step Six: Input the above calculation information into the finite element analysis platform OpenSees, apply in-plane and out-of-plane loading to the model, and obtain the in-plane load-displacement curve, as shown below. Figure 4 As shown, the out-of-plane load-displacement curve is as follows: Figure 5 As shown.

Claims

1. A simplified analysis simulation method for nine-pole infill wall, characterized in that The method comprises the following steps: Step one: determining the nodes 1, 2, 3, 4 of the peripheral vertical and horizontal structural members, determining the two end points 5, 6 and the intermediate node 56 of the intermediate elastic-plastic strut, setting the nodes 51 and 52 and the nodes 61 and 62 at the same positions of the end points 5 and 6 respectively, determining the local nodes 7, 8, 9, 10 of the horizontal structural members, and determining the positions of the end points 5, 6 and the local nodes 7, 8, 9, 10 by the following method: the included angle between the connecting line of the node 2 and the end point 5 and the connecting line of the node 2 and the node 1 is 30-45 degrees, the included angle between the connecting line of the node 1 and the end point 5 and the connecting line of the node 1 and the node 2 is 30-45 degrees, the included angle between the connecting line of the node 3 and the end point 6 and the connecting line of the node 3 and the node 4 is 30-45 degrees, and the included angle between the connecting line of the node 4 and the end point 6 and the connecting line of the node 4 and the node 3 is 30-45 degrees; the distances between the local nodes 7, 8, 9, 10 and the nodes 2, 3, 1, 4 are within 30% of the length of the horizontal structural member, and the intermediate position of the connecting line of the end points 5, 6 is provided with the node 56; Step two: connecting the node 1 and the node 2 to form a structural member 11, connecting the node 3 and the node 4 to form a structural member 12, connecting the node 2 and the node 3 to form a structural member 13, connecting the end point 5, the node 56 and the end point 6 to form an intermediate elastic-plastic strut 14 of the infilled wall, connecting the node 2 and the node 51 to form a rigid strut 15 of the infilled wall, connecting the local node 8 and the node 51 to form a rigid strut 16 of the infilled wall, connecting the local node 7 and the node 61 to form a rigid strut 17 of the infilled wall, connecting the node 3 and the node 61 to form a rigid strut 18 of the infilled wall, connecting the node 1 and the node 52 to form a rigid strut 19 of the infilled wall, connecting the local node 10 and the node 52 to form a rigid strut 20 of the infilled wall, connecting the local node 9 and the node 62 to form a rigid strut 21 of the infilled wall, connecting the node 4 and the node 62 to form a rigid strut 22 of the infilled wall, connecting the node 51 and the end point 5 to form a zero-length unit 23, connecting the node 52 and the end point 5 to form a zero-length unit 24, connecting the node 61 and the end point 6 to form a zero-length unit 25, and connecting the node 62 and the end point 6 to form a zero-length unit 26, to obtain a nine-strut simplified model of the infilled wall; the structural members 11, 12, 13 are given with section and material properties, the zero-length units 23, 24, 25, 26 are given with material properties, and the nine-strut simplified model of the infilled wall is given with boundary conditions, mass and load; Step three: performing fiber discretization on the intermediate elastic-plastic strut of the infilled wall, each fiber representing a small area on the section and having different positions, section areas and material properties, and analyzing the in-plane and out-of-plane coupled seismic responses of the infilled wall.

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