Simplified analysis simulation method for nine-supporting-rod infilled wall

Abstract

The invention discloses a simplified analysis simulation method for a nine-supporting-rod infilled wall, and the method comprises the following steps: 1, determining nodes of peripheral vertical and horizontal structural members, determining two end points and a middle node of a middle elastic-plastic supporting rod, additionally arranging two nodes at the same positions of the two end points respectively, determining local nodes of the horizontal structural member; 2, a filler wall nine-supporting-rod simplified model composed of eight filler wall rigid supporting rods and filler wall middle elastic-plastic supporting rods is constructed; 3, fiber discretization is conducted on the elastic-plastic supporting rod in the middle of the infilled wall, each fiber represents a small area on the cross section and has different positions, cross section areas and material attributes, and the coupling earthquake response inside and outside the plane of the infilled wall is analyzed. The method is mainly used for analyzing the earthquake response inside and outside the infilled wall plane under the earthquake action, the actual working state of the infilled wall can be better reflected under the condition that the accuracy is ensured, and engineering application is facilitated.

Description

Technical Field

[0001] The present invention belongs to the field of building seismic construction, and relates to a simplified analysis and simulation method for infill walls, specifically to an analysis method for the coupled seismic response of infill walls in and out of the plane. Background Art

[0002] The masonry infill wall reinforced concrete frame structure is one of the widely used building structural forms at present. The masonry infill wall is flexibly arranged, which can not only act as the peripheral enclosure structure of the building, but also be used for the partition of the internal space to meet the diversified needs of building functions.

[0003] The equivalent strut simplifies the action of the infill wall into a component similar to a strut. It is usually assumed that the infill wall interacts with the main structure in a certain way (such as stiffness, strength, etc.). By analyzing the mechanical properties of the infill wall, it is transformed into an equivalent strut. In the frame structure, the infill wall often exists as a non-load-bearing wall, but in actual situations, it will affect the overall stability of the frame structure. By regarding the infill wall as an equivalent strut, the stress state of the building can be predicted and analyzed more accurately. Under the action of seismic loads, the infill wall may affect the vibration response of the frame structure. Through the equivalent strut model, the performance of the infill wall under seismic action can be simulated more reasonably. Through the equivalent strut model, the analysis of the action of the infill wall can be greatly simplified, the efficiency of design calculation can be improved, and in structural analysis, the equivalent strut can help ensure that the influence of the infill wall is taken into account, thus avoiding potential structural safety hazards.

[0004] As a non-structural component, the infill wall will undergo a coupled failure mode in and out of the plane during an earthquake. Therefore, a simplified model of the infill wall that can reasonably and effectively reflect the behavior of the infill wall in and out of the plane and the infill wall-frame cooperative working mechanism is crucial for the accuracy and economy of the analysis results. The strut model is the most widely used simplified model for infill walls, but most of these models can only simulate the in-plane mechanical properties of the infill wall. There are few simplified models that consider the coupling effect of the in-plane and out-of-plane mechanical properties of the infill wall, 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 scientific, reasonable and accurate three-dimensional simplified analysis model that can reflect the wall-frame cooperative working mechanism to reveal the typical seismic damage and failure mechanism of the infill wall frame structure. Summary of the Invention

[0005] In order to solve the problem that the existing simulation methods cannot accurately consider the coupling of the in-plane and out-of-plane seismic performance of the infill wall, the present invention provides a simplified analysis and simulation method for a nine-strut infill wall.

[0006] The object of the present invention is achieved through the following technical solutions:

[0007] A simplified analysis and simulation method for a nine-strut infilled wall, comprising the following steps:

[0008] Step 1: Determine the nodes 1, 2, 3, and 4 of the surrounding vertical and horizontal structural members, determine the two endpoints 5 and 6 of the middle elastoplastic struts and the middle node 56, respectively set nodes 51 and 52 as well as 61 and 62 at the same positions of the two endpoints 5 and 6, and 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 endpoints 5, node 56 and endpoint 6 to form the middle elastoplastic strut 14 of the infilled wall, connect node 2 and node 51 to form the rigid strut 15 of the infilled wall, connect node 8 and node 51 to form the rigid strut 16 of the infilled wall, connect node 7 and node 61 to form the rigid strut 17 of the infilled wall, connect node 3 and node 61 to form the rigid strut 18 of the infilled wall, connect node 1 and node 52 to form the rigid strut 19 of the infilled wall, connect node 10 and node 52 to form the rigid strut 20 of the infilled wall, connect node 9 and node 62 to form the rigid strut 21 of the infilled wall, connect node 4 and node 62 to form the rigid strut 22 of the infilled wall, connect node 51 and endpoint 5 to form a zero-length element 23, connect node 52 and endpoint 5 to form a zero-length element 24, connect node 61 and endpoint 6 to form a zero-length element 25, connect node 62 and endpoint 6 to form a zero-length element 26, and obtain the simplified nine-strut model of the infilled wall; Assign cross-section and material properties to structural members 11, 12, and 13, assign material properties to zero-length elements 23, 24, 25, and 26, and assign boundary conditions, mass, and loads to the simplified nine-strut model of the infilled wall;

[0010] Step 3: Discretize the middle elastoplastic strut of the infilled wall into fibers. Each fiber represents a small area on the cross-section and has different positions, cross-sectional areas, and material properties, and analyze the in-plane and out-of-plane coupled seismic response of the infilled wall.

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

[0012] 1. Compared with a single strut, the nine struts in the present invention not only consider the influence of nodes but also consider the influence on the frame beam-columns.

[0013] 2. Compared with a five-strut, no matter the force acting on the nine struts in the present invention is from left to right or from right to left, the struts are in a compressive state, which can better conform to the compressive state of the infilled wall under earthquake action in reality.

[0014] 3. The present invention is mainly used for analyzing the in-plane and out-of-plane seismic responses of infill walls under seismic actions. Under the condition of ensuring accuracy, it can better reflect the actual working state of infill walls and is convenient for engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of a nine-strut infill wall and a schematic diagram of the middle elastoplastic strut;

[0016] Figure 2 It is a schematic diagram of fiber discretization;

[0017] Figure 3 It is a P-M interaction relationship curve;

[0018] Figure 4 It is an in-plane load-displacement curve;

[0019] Figure 5 It is an out-of-plane load-displacement curve. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings, but are not limited thereto. Any modification or equivalent replacement of the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention shall be covered by the protection scope of the present invention.

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

[0022] Step 1: Determine the nodes 1, 2, 3, and 4 of the surrounding vertical and horizontal structural members, determine the two end points 5 and 6 of the middle elastoplastic strut and the middle node 56, respectively set the nodes 51 and 52 as well as 61 and 62 at the same positions of the two end points 5 and 6, and 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 the two end points 5, 6 and the local nodes 7, 8, 9, 10 is as follows: the included angle between the line connecting the node 2 and the end point 5 and the line connecting the node 2 and the node 1 is 30-45 degrees, the included angle between the line connecting the node 1 and the end point 5 and the line connecting the node 1 and the node 2 is 30-45 degrees, the included angle between the line connecting the node 3 and the end point 6 and the line connecting the node 3 and the node 4 is 30-45 degrees, the included angle between the line connecting the node 4 and the end point 6 and the line connecting the node 4 and the node 3 is 30-45 degrees; the distances between the 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 node 56 is set at the middle position of the line connecting the two end points 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 in-filled wall intermediate elastoplastic strut 14, connect node 2 and node 51 to form the in-filled wall rigid strut 15, connect node 8 and node 51 to form the in-filled wall rigid strut 16, connect node 7 and node 61 to form the in-filled wall rigid strut 17, connect node 3 and node 61 to form the in-filled wall rigid strut 18, connect node 1 and node 52 to form the in-filled wall rigid strut 19, connect node 10 and node 52 to form the in-filled wall rigid strut 20, connect node 9 and node 62 to form the in-filled wall rigid strut 21, connect node 4 and node 62 to form the in-filled wall rigid strut 22, connect node 51 and endpoint 5 to form the zero-length element 23, connect node 52 and endpoint 5 to form the zero-length element 24, connect node 61 and endpoint 6 to form the zero-length element 25, connect node 62 and endpoint 6 to form the zero-length element 26, and obtain the nine-strut simplified model of the in-filled wall. Assign cross-section and material properties to structural members 11, 12, and 13, assign material properties to zero-length elements 23, 24, 25, and 26, and assign boundary conditions, mass, and loads to the model.

[0025] In this step, the nine-strut simplified model of the in-filled wall consists of 8 in-filled wall rigid struts and the in-filled wall intermediate elastoplastic strut. One node of the 8 in-filled wall rigid struts is the node of the structural member, and the other node is connected to the in-filled wall intermediate elastoplastic strut through a zero-length element, as Figure 1 shown. The in-filled wall intermediate elastoplastic strut is divided into two elements and connected by a central node. Among them, the in-filled wall intermediate elastoplastic strut can not only bear axial pressure but also simulate bending deformation, realizing the unified description of the in-filled wall's in-plane and out-of-plane actions, so as to more accurately simulate the nonlinear mechanical behavior of the in-filled wall. Four zero-length elements are introduced at both ends of the in-filled wall intermediate elastoplastic strut to connect the in-filled wall intermediate elastoplastic strut and the in-filled wall rigid strut. Each zero-length element contains 6 degrees of freedom. Among them, in the horizontal direction in the plane, the compressive strength is infinite, the tensile strength is infinitesimal, and the other five degrees of freedom are infinite.

[0026] Step 3: Discretize the in-filled wall intermediate elastoplastic strut into fibers. Each fiber represents a small area on the cross-section, with different positions, cross-sectional areas, and material properties, and analyze the in-filled wall's in-plane and out-of-plane coupled seismic response.

[0027] In this step, as Figure 2 shown, the method for discretizing the in-filled wall intermediate elastoplastic strut into fibers is:

[0028] As Figure 1As shown, when the infill wall is subjected to in-plane loads from left to right, the rigid struts of the blue infill wall are compressed, and the rigid struts of the red infill wall are ineffective. At this time, the beam-column elements at the center are compressed. On the contrary, when the infill wall is subjected to in-plane loads from right to left, the rigid struts of the red infill wall are compressed, and the beam-column elements at the center are still compressed, thus simulating the compressed state of the infill wall under earthquake action. In order to enable the simplified model to accurately reflect the mechanical properties of the infill wall under pure in-plane loads, it is necessary to simplify the in-plane force-displacement relationship of the infill wall and determine the axial force-displacement relationship of the elastoplastic strut in the middle of the infill wall through geometric transformation.

[0029] Calculation method of in-plane bearing capacity P of the nine-strut simplified model of the infill wall n0 is as follows:

[0030] P n0 = Q ce × A n (1)

[0031] A n = t inf × L inf (2)

[0032]

[0033] Where: P n0 is the in-plane bearing capacity; Q ce is the horizontal shear capacity; A n is the masonry infill area; t inf is the thickness of the infill wall; L inf is the length of the infill wall; V te is the shear strength of the masonry.

[0034] The out-of-plane mechanical characteristics of the infill wall are reflected by the bending of the elastoplastic strut in the middle of the infill wall out of the plane. When an out-of-plane external force is applied at the central node, the elastoplastic strut in the middle of the infill wall and the zero-length element become particularly important, and they determine the bending stiffness and failure mode of the wall. In order to accurately depict the mechanical behavior of the infill wall under pure out-of-plane loads, the key lies in ensuring that the maximum out-of-plane bending bearing capacity of the elastoplastic strut in the middle of the infill wall matches the actual out-of-plane bearing capacity of the infill wall. At the same time, in this state, the deflection of the center point of the elastoplastic strut in the middle of the infill wall should also be consistent with the out-of-plane displacement of the center point of the infill wall. Given that the nine-strut simplified model of the infill wall can be regarded as a simply supported beam with a concentrated mass at the mid-span in the out-of-plane direction, while the actual infill wall system behaves as a simply supported beam with a distributed mass, in order to make the first natural frequencies of the two equal, the equivalent mass of the infill wall set at the central node of the nine-strut simplified model of the infill wall in the present invention is adjusted to 81% of the self-weight of the infill wall.

[0035] Determine the out-of-plane flexural bearing capacity of the elastoplastic strut in the middle of the infill wall:

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

[0037]

[0038] In the formula, M eq is the out-of-plane flexural bearing capacity of the simplified nine-strut model of the infill wall; L is the length of the simplified nine-strut model of the infill wall; M y is the out-of-plane flexural bearing capacity of the infill wall; h inf is the height of the infill wall; q in is the uniformly distributed load acting on the infill wall out-of-plane; f’ me is the compressive strength of the masonry; λ2 is taken as 0.04.

[0039] Determine the sectional moment of inertia of the elastoplastic strut in the middle of the infill wall:

[0040] Based on the relationship between the central deflection of the simplified nine-strut model of the infill wall, that is, the amount of 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:

[0041]

[0042] MEW = 0.81W inf (9)

[0043] W inf = γ inf ·t inf ·h inf ·L inf (10)

[0044]

[0045] w inf = γ inf ·t inf ·L inf (13)

[0046] In the formula, I eq is the sectional moment of inertia of the elastoplastic strut in the middle of the infill wall; K eq is the secant stiffness corresponding to the out-of-plane bearing capacity of the infill wall; E m is the elastic modulus of the infill wall; MEW is the out-of-plane effective weight; W inf is the total weight of the infill wall; γ inf is the unit weight of the infill wall; fss is the first-order vibration frequency of the infill wall; g is the acceleration due to gravity; I inf is the moment of inertia of the cross-section of the infill wall in the initial cracking state; w inf is the weight per unit length of the infill wall.

[0047] To simulate the in-plane and out-of-plane interaction of the infill wall under bi-directional loads, the cross-section of the middle elastoplastic strut of the nine-strut simplified model of the infill wall was carefully designed. In the out-of-plane direction, the cross-section of the middle elastoplastic strut of the infill wall was discretized into n fibers, and each fiber represents a specific small area on the cross-section. These areas have different positions, cross-sectional areas, and material properties. Such a design enables the present 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 cross-section of the middle elastoplastic strut of the infill wall will change dynamically, especially its movement in the out-of-plane direction, which will directly lead to corresponding changes in its in-plane axial bearing capacity and out-of-plane flexural bearing capacity. This change is an intuitive manifestation of the in-plane and out-of-plane interaction of the infill wall. When the axial force on the cross-section of the middle elastoplastic strut of the infill wall gradually increases, the neutral axis tends to move towards the compressed side. This movement will further affect the stress distribution state of each fiber, and may further lead to a decrease in the flexural bearing capacity of the entire cross-section. Similarly, the change in the bending moment on the cross-section of the middle elastoplastic strut of the infill wall will also have a significant impact on the stress-strain state of each fiber. This process of mutual influence and dynamic adjustment enables the present invention to more comprehensively understand and predict the overall mechanical properties of the infill wall under complex load conditions. In summary, by discretizing the cross-section of the middle elastoplastic strut of the infill wall and considering the combined action of in-plane and out-of-plane loads, the in-plane and out-of-plane interaction of the infill wall can be more accurately simulated, providing strong support for structural design and analysis.

[0048] Determine the fiber parameters after discretizing the cross-section of the middle elastoplastic strut of the infill wall:

[0049] As Figure 3 shown, through the interaction relationship curve between the in-plane axial bearing capacity P and the out-of-plane flexural bearing capacity M of the infill wall under in-plane and out-of-plane loads, the position and peak bearing capacity of each fiber can be determined, and the calculation formula is as follows:

[0050]

[0051] In the formula, i is the discrete point sequence. When i = 1, the out-of-plane bending moment on the P-M interaction curve is 0; F yi is the peak bearing capacity of the i-th fiber; P i is the in-plane axial bearing capacity corresponding to the i-th discrete point on the P-M interaction curve; Z iis the distance between the ith fiber and the center of the wall section along the out-of-plane direction; M i is the out-of-plane bending capacity corresponding to the i-th discrete point on the PM interaction curve.

[0052] Therefore, the peak stress and peak strain of each fiber can be calculated according to equations (8) and (9):

[0053]

[0054] In the formula, σ yi is the peak stress of the ith fiber; A i is the area of ​​the i-th fiber; ε i is the peak strain of the ith fiber.

[0055] The cross-sectional area of ​​the discrete fiber 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 section is the same as the moment of inertia of the elastic-plastic strut in the middle of the infill wall. By combining the following formulas, the cross-sectional area of ​​each fiber can be obtained:

[0056]

[0057] Where N is the number of fibers on one side of the z-axis; t m is the thickness of the infill wall; a is the width of the elastic-plastic support rod in the middle of the infill wall.

[0058] Example:

[0059] This example provides a single-layer single-span reinforced concrete frame with a layer height of 1700mm, a span of 2300mm, a filling wall thickness of 100mm, a height of 1400mm, a width of 2100mm, and a length of the elastic-plastic brace in the middle of the filling wall of 1045mm.

[0060] Step 1: In the Opensees finite element software, create the corresponding reinforced concrete frame model by defining geometric parameters, defining node coordinates, defining beam-column sections, defining beam-column units, defining loads, and other commands.

[0061] Step 2: The in-plane bearing capacity P of the simplified model of the infill wall with nine braces n0 Calculate, where V te 0.23mpa, P ce Take 50kN and calculate P n0 It is 46.75kN.

[0062] Step 3: Calculate the out-of-plane bending capacity of the simplified model of the infill wall with nine braces. The out-of-plane uniform load resultant is 60 kN, that is, M yIt is 10.5 kN·m, and from this, the out-of-plane flexural bearing capacity of the simplified model of the nine-strut infill wall is obtained as 12.31 kN·m.

[0063] Step 4: Calculate the out-of-plane moment of inertia of the simplified model of the nine-strut infill wall. The elastic modulus is 1260 MPa, and the calculated out-of-plane moment of inertia is 5887.47 cm 4 .

[0064] Step 5: In the out-of-plane direction, discretize the elastoplastic strut section into 10 fibers. Each fiber represents a specific small area on the section, and these areas have different positions, cross-sectional areas, and material properties. Through the interaction relationship curve between the in-plane axial bearing capacity P and the out-of-plane flexural bearing capacity M of the infill wall under in-plane and out-of-plane loads, the position z and peak strength σ of each fiber can be determined, as shown in Tables 1 and 2.

[0065] Table 1

[0066] z1 864.362 z2 476.25 z3 321.564 z4 232.41 z5 121.412 z6 -121.412 z7 -232.41 z8 -321.564 z9 -476.25 z10 -864.362

[0067] Table 2

[0068] σ1 0.09 σ2 0.15 σ3 0.2 σ4 0.26 σ5 0.43 σ6 0.43 σ7 0.26 σ8 0.2 σ9 0.15 σ10 0.09

[0069] Step 6: Input the above calculation information into the finite element analysis platform OpenSees, apply in-plane and out-of-plane loads to the model, and obtain the in-plane load-displacement curve, as Figure 4 shown, and the out-of-plane load-displacement curve, as Figure 5 shown.

Claims

1. A simplified analysis and simulation method for a nine-strut infilled wall, characterized in that The method includes the following steps: Step 1: Determine nodes 1, 2, 3, and 4 of the surrounding vertical and horizontal structural members, determine the two endpoints 5 and 6 of the intermediate elastoplastic strut and the intermediate node 56. Set nodes 51 and 52 as well as 61 and 62 at the same positions of the two endpoints 5 and 6 respectively, and determine the local nodes 7, 8, 9, and 10 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 12, connect node 2 and node 3 to form structural member 13, connect endpoints 5, node 56, and endpoint 6 to form the intermediate elastoplastic strut 14 of the infill wall, connect node 2 and node 51 to form the rigid strut 15 of the infill wall, connect node 8 and node 51 to form the rigid strut 16 of the infill wall, connect 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 node 10 and node 52 to form the rigid strut 20 of the infill wall, connect node 9 and node 62 to form the rigid strut 21 of the infill wall, connect node 4 and node 62 to form the rigid strut 22 of the infill wall, connect node 51 and endpoint 5 to form the zero-length element 23, connect node 52 and endpoint 5 to form the zero-length element 24, connect node 61 and endpoint 6 to form the zero-length element 25, connect node 62 and endpoint 6 to form the zero-length element 26, and obtain the simplified model of the nine-strut infill wall; Assign section and material properties to structural members 11, 12, and 13, assign material properties to zero-length elements 23, 24, 25, and 26, and assign boundary conditions, mass, and loads to the simplified model of the nine-strut infill wall. Step 3: Discretize the intermediate elastoplastic strut of the infill wall into fibers. Each fiber represents a small area on the cross-section and has different positions, cross-sectional areas, and material properties, and analyze the in-plane and out-of-plane coupled seismic response of the infill wall.

2. The simplified analysis and simulation method of the nine-strut infilled wall according to claim 1, wherein In the above Step 1, the method for determining the positions of the two endpoints 5, 6 and the local nodes 7, 8, 9, 10 is as follows: The included angle between the line connecting node 2 and endpoint 5 and the line connecting node 2 and node 1 is 30 - 45 degrees, the included angle between the line connecting node 1 and endpoint 5 and the line connecting node 1 and node 2 is 30 - 45 degrees, the included angle between the line connecting node 3 and endpoint 6 and the line connecting node 3 and node 4 is 30 - 45 degrees, the included 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 nodes 7, 8, 9, 10 and nodes 2, 3, 1, 4 respectively are within 30% of the length of the horizontal structural member, and node 56 is set at the middle position of the line connecting the two endpoints 5 and 6.

3. The simplified analysis and simulation method of the nine-strut infilled wall according to claim 1, characterized in that In the above Step 2, each zero-length element contains 6 degrees of freedom. Among them, in the horizontal direction in the plane, the compressive strength is infinite, the tensile strength is infinitesimal, and the other five degrees of freedom are infinite.

4. The simplified analysis and simulation method for a nine-strut infilled wall according to claim 1, characterized in that In the above Step 3, the method for discretizing the intermediate elastoplastic strut of the infill wall into fibers is as follows: (1) Calculate the in-plane bearing capacity P of the simplified model of the nine struts of the infill wall n0 : P n0 = Q ce × A n A n = t inf × L inf Where: P n0 is the bearing capacity in the plane; Q ce is the horizontal shear capacity; A n is the masonry filling area; t inf is the thickness of the infill wall; L inf is the length of the infill wall; V te is the shear strength of the masonry; (2) Determine the out-of-plane flexural bearing capacity of the intermediate elastoplastic strut of the infill wall: The relationship between the out-of-plane bending capacity of the simplified nine-strut model of the infill wall and the out-of-plane bending capacity of the infill wall is shown below: Where M eq is the out-of-plane flexural bearing capacity of the simplified model of the nine struts of the infill wall; L is the length of the simplified model of the nine struts of the infill wall; M y is the out-of-plane flexural bearing capacity of the infill wall; h inf is the height of the infill wall; (3) Determine the section moment of inertia of the elastic-plastic strut in the middle of the infill wall: According to the relationship between the center point deflection of the simplified model of the infill wall with nine braces, that is, the bending deformation of the simplified model of the infill wall with nine braces, 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 model of the infill wall with nine braces is established: Where, I eq is the sectional moment of inertia of the elastoplastic strut in the middle of the infill wall; K eq is the secant stiffness corresponding to the out-of-plane bearing capacity of the infill wall; E m is 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 represents 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 elastic-plastic strut cross section in the infill wall: The position and peak strength of each fiber are determined by the interaction curve between the in-plane axial bearing capacity P and the out-of-plane bending bearing capacity M of the infill wall under in-plane and out-of-plane loads. The calculation formula is as follows: where \(i\) is the discrete point sequence. When \(i = 1\), the out-of-plane bending moment on the P-M interaction curve is 0; \(F\) yi is the peak bearing capacity of the \(i\)-th fiber; \(P\) i is the in-plane axial bearing capacity corresponding to the \(i\)-th discrete point on the P-M interaction curve; \(Z\) i is the distance between the \(i\)-th fiber and the center of the wall section in the out-of-plane direction; \(M\) i is the out-of-plane flexural bearing capacity corresponding to the \(i\)-th discrete point on the P-M interaction curve; Therefore, the peak stress and peak strain of each fiber are calculated according to equations (8) and (9): Where, σ yi is the peak stress of the i-th fiber; A i is the area of the i-th fiber; ε i is the peak strain of the i-th fiber; (6) The cross-sectional area of ​​each fiber is obtained by combining the following equations: Where N is the number of fibers on one side of the z-axis; t m is the thickness of the infill wall; a is the width of the elastoplastic strut in the middle of the infill wall.

5. The simplified analysis and simulation method of the nine-strut infilled wall according to claim 4, characterized in that In (2) above, the out-of-plane flexural bearing capacity M of the infill wall y is calculated as follows: where q in is the uniformly distributed load perpendicular to the plane of the infill wall; f ’ me is the compressive strength of the masonry; λ2 is taken as 0.

04.

6. The simplified analysis and simulation method for a nine-strut infilled wall according to claim 4, wherein In the above (3), the secant stiffness K corresponding to the out-of-plane bearing capacity of the infill wall eq is calculated as follows: MEW = 0.81W inf W inf = γ inf · t inf · h inf · L inf w inf = γ inf · t inf · L inf Where, W inf is the total weight of the infill wall; γ inf is the unit weight of the infill wall; f ss is the first-order vibration frequency of the infill wall; g is the acceleration due to gravity; I inf is the moment of inertia of the cross-section of the infill wall in the initial cracking state; w inf is the weight per unit length of the infill wall.

7. The simplified analysis and simulation method of the nine-strut infilled wall according to claim 4, 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 the individual fibers is consistent with the cross-sectional area of ​​the elastic-plastic struts in the middle of the infill wall; 2) The moment of inertia of the discretized fiber section is the same as the moment of inertia of the elastic-plastic struts in the middle of the infill wall.

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