# A Simplified Finite Element Model for Modular Steel Structure Building Wallboard through Experimental Research and Finite Element Analysis

Authors: Jun Cong; Shanzuo Zheng; Bing Lin; Lei Zhang; Lin Peng
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

The traditional research on steel plate shear wall structure mainly focuses on the overall performance of the wall, and the mechanical properties of the connection between plates and plates and between plates and frames are not clear. In this paper, the experimental research on the wallboard structure of bending plate was carried out and the mechanical properties and failure modes of five walls were analyzed. In addition, the connection properties between plates and frames were studied by finite element analysis. A simplified finite element model is presented by experimental study and finite element analysis. The results show that the finite element analysis results are in good agreement with the experimental results. The finite element model with the two-point binding constraint between the end of the bending plate and the angle steel can well simulate the mechanical properties of the steel plate shear wall structure.


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## Body

## 1. Introduction

With the development of building industrialization, it has become the consensus of building industry to vigorously develop modular building structure. Modular wallboard structure can be used as the lateral load resisting member and the energy dissipation components, which is the first line of defense for seismic fortification of the structure [1–5]. However, the research on modular wallboard structure mainly focuses on the overall performance of the wall. How to consider the mechanical properties of the connection between plate and plate and between plate and frame to improve the efficiency of calculation is urgent problem to be solved.Cao and Huang [6] carried out theoretical analysis of corrugated steel plate shear wall and assumed that the plate was a trilinear model and the frame was completely plastic and then proposed that the calculation results of the plate-frame interaction model were more similar to the experimental results. Zeng [7] studied the calculation of lateral stiffness of corrugated plate of container structure with and without holes. Wang [8] studied the whole process mechanical properties of corrugated plate against impact and explosion. Yin [9] analyzed the lateral and longitudinal stiffness of a new modular housing box-type integrated house under external load. Cha [10, 11] optimized the container structure based on the use of finite element software. Yang and Mou [12], Zuo [13, 14], Qiu [15], and Zhang [16] et al. defined the connections between components in the model by means of Tie. The above research on steel plate shear walls has been very in-depth, but most of them are steel plate shear walls with corrugated plates. The connection is usually fully welded or discontinuous welded, and the research on bending plate is relatively little [17]. As the main internal maintenance component, bending plate is mostly used in indoor buildings, which accounts for a large proportion. Therefore, it is necessary to conduct in-depth research on the mechanical properties of bending plate shear wall.For subsequent parametric analysis, a finite element model that can reflect the actual mechanical properties of the structure and ensure the reliability of the calculated results is urgently needed. Therefore, in this paper, the mechanical properties and failure modes of the modular wallboard structure are tested and analyzed. And the influence of differentbinding forms of finite element analysis model on the calculation results is analyzed. Through the comparison between the calculated results and experimental results, the two-point binding constraint between the bending plate and angle steel can better reflect the mechanical properties of modular wall structure.


## 2. Method

### 2.1. Experimental Method

#### 2.1.1. Experimental Model

The module size is 5 m (L)∗ 3.48 m (W) ∗ 3.42 m (H), for the short wallboard, it is 3.48 m (W) ∗ 3.42 (H), and the long wallboard size is 5 m (L) ∗ 3.42 m (H). The experiment was conducted at the China State Construction Technical Center; some photos of the experiments are shown in Figure 1.Figure 1
Experimental photos.The specimen boundary and loading condition are shown in Figure2. The corner pieces at the bottom of the wallboard are consolidated, and unidirectional horizontal load is applied to the top of the column. A lateral resistance device is arranged in the middle or three points of the top beam.Figure 2
Boundary condition.Three groups of specimens are designed with seven pieces of walls. The test groups are shown in Table1, and the specimen models are shown in Figures 3–7.Table 1
Specimen grouping.
GroupSpecimen numberNumberDescriptionFirst groupQKX-11The short wallboard, pure frameSecond groupQX-11The short wallboard, one holeQX-21The short wallboard, two holesThird groupQY-11The long wallboard, without the holeQY-21The long wallboard, without the holeFigure 3
Model of QKX-1.Figure 4
Model of QX-1.Figure 5
Model of QX-2.Figure 6
Model of QY-1.Figure 7
Model of QY-2.


#### 2.1.2. Test Loading Scheme

Firstly, preloading is carried out to check the working condition of the equipment and ensure that the test device and observation and acquisition instruments are all in normal working state. Then start the formal loading and each level of load to take 5% of the calculated ultimate load. When buckling deformation appears or the load reaches 80% of the ultimate load, the loading amplitude decreases.When there is a large deformation of the specimen or a sudden change in the displacement and strain, the each level of load should be more small. The data and experimental phenomena of each loading stage should be recorded until the load reached the maximum value. In order to obtain the descending section of load-displacement curve, loading should be continued after the load reaches the maximum value until the load drops to 85% of the ultimate load. Each level of load was applied for two minutes with data collection. All data should be collected by static resistance strain tester. The loading model is shown in Figure8.Figure 8
Loading model of wallboard.


### 2.2. The Finite Element Model

#### 2.2.1. Calculation Illustration

(1)
The finite element software ABAQUS was used to analyze the mechanical properties of the wallboard. The beam-column members, corner pieces, and wallboard were modeled by solid units. The structure size is consistent with the size in experiment.(2)
Second-order elastic large deformation algorithm was used.(3)
The steel constitutive model adopts ideal elastic-plastic model without considering steel reinforcement.(4)
The unit type of the elements of beam-column members, corner pieces, and wallboard is all C3D4, namely, four-node linear tetrahedron element.


#### 2.2.2. Interaction and the Load Settings

For the QKX-1, the beams, columns, and corner pieces are bound together, and the bottom of the frame, that is, bottom corner piece is consolidated, and horizontal loading is applied at the midpoint of the top corner piece. The loading adopts the point-coupled surface loading form to prevent stress concentration on the loading surface. The interaction and loading settings of QKX-1 are shown in Figure9.Figure 9
Interaction and loading settings of QKX-1. (a) Beam-column connection. (b) Consolidated corner piece. (c) Point-coupled surface loading.
(a)(b)(c)The binding forms of QX-1 and QX-2 are the same. The frame and the angle steel are connected by surface binding, the angle steel of the window side is bound to the corresponding position of the frame column, and the inner surface of the top and bottom of the frame is bound to the outer surface of bottom of the angle steel. The connection between the top and bottom of the bending plate and the angle steel is node binding. Two-point binding form is set between each end of the bending plate and the angle steel. The QX-1 and QX-2 model binding forms are shown in Figures10 and 11, respectively.Figure 10
Binding forms of QX-1. (a) Surface binding of angle steel by the window. (b) Surface binding of end angle steel. (c) Point binding for bending plate.
(a)(b)(c)Figure 11
Binding forms of QX-2. (a) Surface binding of angle steel by the window. (b) Surface binding of end angle steel. (c) Point binding for bending plate.
(a)(b)(c)QY-1 and QY-2 calculation model components are composed of frame (2 square tubes, 4 corner pieces, and 2 angle steel), bending plate, and angle steel. The frame and the angle steel are connected by surface binding. The connection between the top and bottom of the bending plate and the angle steel is point binding. Two-point binding form is set between each end of the bending plate and the angle steel. The QY-1 and QY-2 model binding forms are shown in Figures12 and 13, respectively.Figure 12
Binding forms of QY-1. (a) Surface binding of angle steel. (b) Point binding of bending plate.
(a)(b)Figure 13
Binding forms of QY-2. (a) Surface binding of angle steel. (b) Point binding of bending plate.
(a)(b)


## 2.1. Experimental Method

### 2.1.1. Experimental Model

The module size is 5 m (L)∗ 3.48 m (W) ∗ 3.42 m (H), for the short wallboard, it is 3.48 m (W) ∗ 3.42 (H), and the long wallboard size is 5 m (L) ∗ 3.42 m (H). The experiment was conducted at the China State Construction Technical Center; some photos of the experiments are shown in Figure 1.Figure 1
Experimental photos.The specimen boundary and loading condition are shown in Figure2. The corner pieces at the bottom of the wallboard are consolidated, and unidirectional horizontal load is applied to the top of the column. A lateral resistance device is arranged in the middle or three points of the top beam.Figure 2
Boundary condition.Three groups of specimens are designed with seven pieces of walls. The test groups are shown in Table1, and the specimen models are shown in Figures 3–7.Table 1
Specimen grouping.
GroupSpecimen numberNumberDescriptionFirst groupQKX-11The short wallboard, pure frameSecond groupQX-11The short wallboard, one holeQX-21The short wallboard, two holesThird groupQY-11The long wallboard, without the holeQY-21The long wallboard, without the holeFigure 3
Model of QKX-1.Figure 4
Model of QX-1.Figure 5
Model of QX-2.Figure 6
Model of QY-1.Figure 7
Model of QY-2.


### 2.1.2. Test Loading Scheme

Firstly, preloading is carried out to check the working condition of the equipment and ensure that the test device and observation and acquisition instruments are all in normal working state. Then start the formal loading and each level of load to take 5% of the calculated ultimate load. When buckling deformation appears or the load reaches 80% of the ultimate load, the loading amplitude decreases.When there is a large deformation of the specimen or a sudden change in the displacement and strain, the each level of load should be more small. The data and experimental phenomena of each loading stage should be recorded until the load reached the maximum value. In order to obtain the descending section of load-displacement curve, loading should be continued after the load reaches the maximum value until the load drops to 85% of the ultimate load. Each level of load was applied for two minutes with data collection. All data should be collected by static resistance strain tester. The loading model is shown in Figure8.Figure 8
Loading model of wallboard.


## 2.1.1. Experimental Model

The module size is 5 m (L)∗ 3.48 m (W) ∗ 3.42 m (H), for the short wallboard, it is 3.48 m (W) ∗ 3.42 (H), and the long wallboard size is 5 m (L) ∗ 3.42 m (H). The experiment was conducted at the China State Construction Technical Center; some photos of the experiments are shown in Figure 1.Figure 1
Experimental photos.The specimen boundary and loading condition are shown in Figure2. The corner pieces at the bottom of the wallboard are consolidated, and unidirectional horizontal load is applied to the top of the column. A lateral resistance device is arranged in the middle or three points of the top beam.Figure 2
Boundary condition.Three groups of specimens are designed with seven pieces of walls. The test groups are shown in Table1, and the specimen models are shown in Figures 3–7.Table 1
Specimen grouping.
GroupSpecimen numberNumberDescriptionFirst groupQKX-11The short wallboard, pure frameSecond groupQX-11The short wallboard, one holeQX-21The short wallboard, two holesThird groupQY-11The long wallboard, without the holeQY-21The long wallboard, without the holeFigure 3
Model of QKX-1.Figure 4
Model of QX-1.Figure 5
Model of QX-2.Figure 6
Model of QY-1.Figure 7
Model of QY-2.


## 2.1.2. Test Loading Scheme

Firstly, preloading is carried out to check the working condition of the equipment and ensure that the test device and observation and acquisition instruments are all in normal working state. Then start the formal loading and each level of load to take 5% of the calculated ultimate load. When buckling deformation appears or the load reaches 80% of the ultimate load, the loading amplitude decreases.When there is a large deformation of the specimen or a sudden change in the displacement and strain, the each level of load should be more small. The data and experimental phenomena of each loading stage should be recorded until the load reached the maximum value. In order to obtain the descending section of load-displacement curve, loading should be continued after the load reaches the maximum value until the load drops to 85% of the ultimate load. Each level of load was applied for two minutes with data collection. All data should be collected by static resistance strain tester. The loading model is shown in Figure8.Figure 8
Loading model of wallboard.


## 2.2. The Finite Element Model

### 2.2.1. Calculation Illustration

(1)
The finite element software ABAQUS was used to analyze the mechanical properties of the wallboard. The beam-column members, corner pieces, and wallboard were modeled by solid units. The structure size is consistent with the size in experiment.(2)
Second-order elastic large deformation algorithm was used.(3)
The steel constitutive model adopts ideal elastic-plastic model without considering steel reinforcement.(4)
The unit type of the elements of beam-column members, corner pieces, and wallboard is all C3D4, namely, four-node linear tetrahedron element.


### 2.2.2. Interaction and the Load Settings

For the QKX-1, the beams, columns, and corner pieces are bound together, and the bottom of the frame, that is, bottom corner piece is consolidated, and horizontal loading is applied at the midpoint of the top corner piece. The loading adopts the point-coupled surface loading form to prevent stress concentration on the loading surface. The interaction and loading settings of QKX-1 are shown in Figure9.Figure 9
Interaction and loading settings of QKX-1. (a) Beam-column connection. (b) Consolidated corner piece. (c) Point-coupled surface loading.
(a)(b)(c)The binding forms of QX-1 and QX-2 are the same. The frame and the angle steel are connected by surface binding, the angle steel of the window side is bound to the corresponding position of the frame column, and the inner surface of the top and bottom of the frame is bound to the outer surface of bottom of the angle steel. The connection between the top and bottom of the bending plate and the angle steel is node binding. Two-point binding form is set between each end of the bending plate and the angle steel. The QX-1 and QX-2 model binding forms are shown in Figures10 and 11, respectively.Figure 10
Binding forms of QX-1. (a) Surface binding of angle steel by the window. (b) Surface binding of end angle steel. (c) Point binding for bending plate.
(a)(b)(c)Figure 11
Binding forms of QX-2. (a) Surface binding of angle steel by the window. (b) Surface binding of end angle steel. (c) Point binding for bending plate.
(a)(b)(c)QY-1 and QY-2 calculation model components are composed of frame (2 square tubes, 4 corner pieces, and 2 angle steel), bending plate, and angle steel. The frame and the angle steel are connected by surface binding. The connection between the top and bottom of the bending plate and the angle steel is point binding. Two-point binding form is set between each end of the bending plate and the angle steel. The QY-1 and QY-2 model binding forms are shown in Figures12 and 13, respectively.Figure 12
Binding forms of QY-1. (a) Surface binding of angle steel. (b) Point binding of bending plate.
(a)(b)Figure 13
Binding forms of QY-2. (a) Surface binding of angle steel. (b) Point binding of bending plate.
(a)(b)


## 2.2.1. Calculation Illustration

(1)
The finite element software ABAQUS was used to analyze the mechanical properties of the wallboard. The beam-column members, corner pieces, and wallboard were modeled by solid units. The structure size is consistent with the size in experiment.(2)
Second-order elastic large deformation algorithm was used.(3)
The steel constitutive model adopts ideal elastic-plastic model without considering steel reinforcement.(4)
The unit type of the elements of beam-column members, corner pieces, and wallboard is all C3D4, namely, four-node linear tetrahedron element.


## 2.2.2. Interaction and the Load Settings

For the QKX-1, the beams, columns, and corner pieces are bound together, and the bottom of the frame, that is, bottom corner piece is consolidated, and horizontal loading is applied at the midpoint of the top corner piece. The loading adopts the point-coupled surface loading form to prevent stress concentration on the loading surface. The interaction and loading settings of QKX-1 are shown in Figure9.Figure 9
Interaction and loading settings of QKX-1. (a) Beam-column connection. (b) Consolidated corner piece. (c) Point-coupled surface loading.
(a)(b)(c)The binding forms of QX-1 and QX-2 are the same. The frame and the angle steel are connected by surface binding, the angle steel of the window side is bound to the corresponding position of the frame column, and the inner surface of the top and bottom of the frame is bound to the outer surface of bottom of the angle steel. The connection between the top and bottom of the bending plate and the angle steel is node binding. Two-point binding form is set between each end of the bending plate and the angle steel. The QX-1 and QX-2 model binding forms are shown in Figures10 and 11, respectively.Figure 10
Binding forms of QX-1. (a) Surface binding of angle steel by the window. (b) Surface binding of end angle steel. (c) Point binding for bending plate.
(a)(b)(c)Figure 11
Binding forms of QX-2. (a) Surface binding of angle steel by the window. (b) Surface binding of end angle steel. (c) Point binding for bending plate.
(a)(b)(c)QY-1 and QY-2 calculation model components are composed of frame (2 square tubes, 4 corner pieces, and 2 angle steel), bending plate, and angle steel. The frame and the angle steel are connected by surface binding. The connection between the top and bottom of the bending plate and the angle steel is point binding. Two-point binding form is set between each end of the bending plate and the angle steel. The QY-1 and QY-2 model binding forms are shown in Figures12 and 13, respectively.Figure 12
Binding forms of QY-1. (a) Surface binding of angle steel. (b) Point binding of bending plate.
(a)(b)Figure 13
Binding forms of QY-2. (a) Surface binding of angle steel. (b) Point binding of bending plate.
(a)(b)


## 3. Results

### 3.1. Comparison of Calculation Results and Experimental Results for QKX-1

#### 3.1.1. Comparison of Failure Mode

When the loading displacement angle is about 1/30, it has been observed that the top right corner piece and the beam weld are pulled apart. The final failure mode of QKX-1 is the failure of the weld between the top right corner piece and the tension side of the beam. The loading displacement angle at the time of failure is 1/20; at this time the beam, the corner pieces have been pulled apart in a large area. The calculation results of finite element analysis show that when the model is loaded to the displacement angle of about 1/27, the maximum stress here has been already reached the yield strength. Comparison of failure mode for QKX-1 is shown in Figure14. The load-displacement curves of the QKX-1 with various connection conditions are calculated, as shown in Figure 15.Figure 14
Comparison of failure mode for QKX-1. (a) Experimental results for QKX-1. (b) Calculation results for QKX-1.
(a)(b)Figure 15
Comparison of load-displacement curve for QKX-1.


#### 3.1.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QKX-1 between the calculated results and the experimental results is shown in Table2.Table 2
Comparison of the ultimate bearing capacity and initial stiffness for QKX-1.
Ultimate bearing capacity (kN)Relative errorInitial stiffness (kN/mm)Relative errorExperimental results35.40—0.31—Calculated results32.478.28%0.323.23%From the load-displacement curve of QKX-1, it can be seen that the calculated value is in good agreement with the test value within the range of 1/100 displacement angle, and the calculated value is slightly higher than the experimental value thereafter. This is because the damage to the structure due to welding quality is not considered in the finite element model.


### 3.2. Comparison of Calculation Results and Experimental Results for QX-1

The load-displacement curves of the QX-1 with various connection conditions are calculated, as shown in Figure16. By comparing the load-displacement curve of calculation results of QX-1 with the experimental curve, it is shown that the load-displacement curve obtained by finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 16
Comparison of load-displacement curve for QX-1.Comparison of the ultimate bearing capacity and initial stiffness for QX-1 between the calculated results and the experimental results is shown in Table3.Table 3
Comparison of the ultimate bearing capacity and initial stiffness for QX-1.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results78.11.005.201.00Pure frame in finite element model51.10.651.980.38Two-point binding in finite element model91.21.176.491.25Surface binding in finite element model375.94.8116.493.17From Table3, it can be seen that the initial stiffness of the experimental specimen is 5.20 kN/mm, the bearing capacity is 78.1 kN, the frame model calculated initial stiffness is 1.98 kN/mm, and the bearing capacity is 51.1 kN. That is to say, the wallboard significantly improves the stiffness of the structure by 2.6 times. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 6.49 kN/mm and the bearing capacity is 91.2 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the QX-1 calculated model that is surface-bounded between the angle steel and the bent plate are 3.17 times and 4.81 times better than those of experimental results, respectively. It can be seen that the end connections of the wallboard in the actual structure are weak, resulting in poor overall structure performance, reducing the bearing capacity of the experimental piece, and failing to give full play to the mechanical properties of the material.


### 3.3. Comparison of Calculation Results and Experimental Results for QX-2

#### 3.3.1. Deformation

The load-displacement curves of the QX-2 with various connection conditions are calculated, as shown in Figure17. By comparing the load-displacement curve of calculation results of QX-2 with the experimental curve, it is shown that the load-displacement curve obtained by finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 17
Comparison of load-displacement curve for QX-2.


#### 3.3.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QX-2 between the calculated results and the experimental results is shown in Table4.Table 4
Comparison of the ultimate bearing capacity and initial stiffness for QX-2.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results62.61.004.801.00Pure frame in finite element model70.61.132.620.55Two-point binding in finite element model109.91.765.561.16Surface binding in finite element model344.35.5020.294.23From Table4, it can be seen that the initial stiffness of the experimental specimen is 4.80 kN/mm, the bearing capacity is 62.6 kN, the frame model calculated initial stiffness is 2.62 kN/mm, and the bearing capacity is 70.6 kN. Wallboard can increase the rigidity of the structure. However, large concentrated stresses will be generated in the frame of the test specimen, which will cause premature failure of the weak points and reduce the bearing capacity of the structure. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 5.56 kN/mm and the bearing capacity is 109.9 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the QX-2 calculated model that is surface-bounded between the angle steel and the bent plate are 4.23 times and 5.50 times better than these of experimental results, respectively. It can be seen that increasing the connection strength of the wallboard in the experiment can strengthen the lateral restraint of the wallboard on the structure, especially for the columns in the middle of the frame.


### 3.4. Comparison of Calculation Results and Experimental Results for QY-1

#### 3.4.1. Deformation

The load-displacement curves of the QY-1 with various connection conditions are calculated, as shown in Figure18. By comparing the load-displacement curve of calculation results of QY-1 with the experimental curve, it is shown that the load-displacement curve obtained by the finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 18
Comparison of load-displacement curve for QY-1.


#### 3.4.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QY-1 between the calculated results and the experimental results is shown in Table5.Table 5
Comparison of the ultimate bearing capacity and initial stiffness for QY-1.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results52.61.007.151.00Pure frame in finite element model36.10.691.010.14Two-point binding in finite element model68.81.316.800.95Surface binding in finite element model445.28.4643.536.09From Table5, it can be seen that the initial stiffness of the experimental specimen is 7.15 kN/mm, the bearing capacity is 52.6 kN, the frame model calculated initial stiffness is 1.01 kN/mm, and the bearing capacity is 36.1 kN. It can be concluded that wallboard can increase the rigidity of the structure and also can ensure a certain degree of degeneration ability of the structure. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 6.80 kN/mm and the bearing capacity is 68.8 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the model in which the ends of the bent plate and the angle steel are connected by surface binding are higher than the experimental results. It shows that this type of connection has a significant effect on the overall performance of the structure, and the bent plate has a certain restraint effect on the vertical deformation frame.


### 3.5. Comparison of Calculation Results and Experimental Results for QY-2

#### 3.5.1. Deformation

The load-displacement curves of the QY-2 with various connection conditions are calculated, as shown in Figure19. By comparing the load-displacement curve of calculation results of QY-2 with the experimental curve, it is shown that the load-displacement curve obtained by the finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 19
Comparison of load-displacement curve for QY-2.


#### 3.5.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QY-2 between the calculated results and the experimental results is shown in Table6.Table 6
Comparison of the ultimate bearing capacity and initial stiffness for QY-2.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results65.41.008.301.00Pure frame in finite element model28.20.430.930.11Side contact of bending plate (0.06)497.87.6126.293.17Side contact of bending plate (0.15)517.97.9227.163.27Surface binding in finite element model611.99.3669.898.4250% surface binding in finite element model462.87.0846.416.0025% surface binding in finite element model372.55.7042.835.5912.5% surface binding in finite element model202.33.0925.453.07One-point binding in finite element model30.70.471.040.13Two-point binding in finite element model92.51.4113.811.66Single row node binding in finite element model330.35.0536.964.45Double-row node binding in finite element model744.611.3951.366.18From Table6, it can be seen that the initial stiffness of the experimental specimen is 8.30 kN/mm, the bearing capacity is 65.4 kN, the frame model calculated initial stiffness is 0.93 kN/mm, and the bearing capacity is 28.2 kN. That is to say, the wallboard significantly improves the stiffness of the structure by 8.9 times and bearing capacity by 2.3 times. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 13.81 kN/mm and the bearing capacity is 92.5 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the model in which the ends of the bent plate and the angle steel are connected by double-row node binding are higher than the experimental results. It can be seen that the stiffness of the actual component wallboard is not good enough, and the joint damage in the experiment greatly affects the stiffness and mechanical properties of the experimental specimen. It can be considered to increase the connection strength between the bent plates and between the bent plates and the frame to further improve the mechanical properties of the specimen.


## 3.1. Comparison of Calculation Results and Experimental Results for QKX-1

### 3.1.1. Comparison of Failure Mode

When the loading displacement angle is about 1/30, it has been observed that the top right corner piece and the beam weld are pulled apart. The final failure mode of QKX-1 is the failure of the weld between the top right corner piece and the tension side of the beam. The loading displacement angle at the time of failure is 1/20; at this time the beam, the corner pieces have been pulled apart in a large area. The calculation results of finite element analysis show that when the model is loaded to the displacement angle of about 1/27, the maximum stress here has been already reached the yield strength. Comparison of failure mode for QKX-1 is shown in Figure14. The load-displacement curves of the QKX-1 with various connection conditions are calculated, as shown in Figure 15.Figure 14
Comparison of failure mode for QKX-1. (a) Experimental results for QKX-1. (b) Calculation results for QKX-1.
(a)(b)Figure 15
Comparison of load-displacement curve for QKX-1.


### 3.1.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QKX-1 between the calculated results and the experimental results is shown in Table2.Table 2
Comparison of the ultimate bearing capacity and initial stiffness for QKX-1.
Ultimate bearing capacity (kN)Relative errorInitial stiffness (kN/mm)Relative errorExperimental results35.40—0.31—Calculated results32.478.28%0.323.23%From the load-displacement curve of QKX-1, it can be seen that the calculated value is in good agreement with the test value within the range of 1/100 displacement angle, and the calculated value is slightly higher than the experimental value thereafter. This is because the damage to the structure due to welding quality is not considered in the finite element model.


## 3.1.1. Comparison of Failure Mode

When the loading displacement angle is about 1/30, it has been observed that the top right corner piece and the beam weld are pulled apart. The final failure mode of QKX-1 is the failure of the weld between the top right corner piece and the tension side of the beam. The loading displacement angle at the time of failure is 1/20; at this time the beam, the corner pieces have been pulled apart in a large area. The calculation results of finite element analysis show that when the model is loaded to the displacement angle of about 1/27, the maximum stress here has been already reached the yield strength. Comparison of failure mode for QKX-1 is shown in Figure14. The load-displacement curves of the QKX-1 with various connection conditions are calculated, as shown in Figure 15.Figure 14
Comparison of failure mode for QKX-1. (a) Experimental results for QKX-1. (b) Calculation results for QKX-1.
(a)(b)Figure 15
Comparison of load-displacement curve for QKX-1.


## 3.1.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QKX-1 between the calculated results and the experimental results is shown in Table2.Table 2
Comparison of the ultimate bearing capacity and initial stiffness for QKX-1.
Ultimate bearing capacity (kN)Relative errorInitial stiffness (kN/mm)Relative errorExperimental results35.40—0.31—Calculated results32.478.28%0.323.23%From the load-displacement curve of QKX-1, it can be seen that the calculated value is in good agreement with the test value within the range of 1/100 displacement angle, and the calculated value is slightly higher than the experimental value thereafter. This is because the damage to the structure due to welding quality is not considered in the finite element model.


## 3.2. Comparison of Calculation Results and Experimental Results for QX-1

The load-displacement curves of the QX-1 with various connection conditions are calculated, as shown in Figure16. By comparing the load-displacement curve of calculation results of QX-1 with the experimental curve, it is shown that the load-displacement curve obtained by finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 16
Comparison of load-displacement curve for QX-1.Comparison of the ultimate bearing capacity and initial stiffness for QX-1 between the calculated results and the experimental results is shown in Table3.Table 3
Comparison of the ultimate bearing capacity and initial stiffness for QX-1.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results78.11.005.201.00Pure frame in finite element model51.10.651.980.38Two-point binding in finite element model91.21.176.491.25Surface binding in finite element model375.94.8116.493.17From Table3, it can be seen that the initial stiffness of the experimental specimen is 5.20 kN/mm, the bearing capacity is 78.1 kN, the frame model calculated initial stiffness is 1.98 kN/mm, and the bearing capacity is 51.1 kN. That is to say, the wallboard significantly improves the stiffness of the structure by 2.6 times. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 6.49 kN/mm and the bearing capacity is 91.2 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the QX-1 calculated model that is surface-bounded between the angle steel and the bent plate are 3.17 times and 4.81 times better than those of experimental results, respectively. It can be seen that the end connections of the wallboard in the actual structure are weak, resulting in poor overall structure performance, reducing the bearing capacity of the experimental piece, and failing to give full play to the mechanical properties of the material.


## 3.3. Comparison of Calculation Results and Experimental Results for QX-2

### 3.3.1. Deformation

The load-displacement curves of the QX-2 with various connection conditions are calculated, as shown in Figure17. By comparing the load-displacement curve of calculation results of QX-2 with the experimental curve, it is shown that the load-displacement curve obtained by finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 17
Comparison of load-displacement curve for QX-2.


### 3.3.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QX-2 between the calculated results and the experimental results is shown in Table4.Table 4
Comparison of the ultimate bearing capacity and initial stiffness for QX-2.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results62.61.004.801.00Pure frame in finite element model70.61.132.620.55Two-point binding in finite element model109.91.765.561.16Surface binding in finite element model344.35.5020.294.23From Table4, it can be seen that the initial stiffness of the experimental specimen is 4.80 kN/mm, the bearing capacity is 62.6 kN, the frame model calculated initial stiffness is 2.62 kN/mm, and the bearing capacity is 70.6 kN. Wallboard can increase the rigidity of the structure. However, large concentrated stresses will be generated in the frame of the test specimen, which will cause premature failure of the weak points and reduce the bearing capacity of the structure. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 5.56 kN/mm and the bearing capacity is 109.9 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the QX-2 calculated model that is surface-bounded between the angle steel and the bent plate are 4.23 times and 5.50 times better than these of experimental results, respectively. It can be seen that increasing the connection strength of the wallboard in the experiment can strengthen the lateral restraint of the wallboard on the structure, especially for the columns in the middle of the frame.


## 3.3.1. Deformation

The load-displacement curves of the QX-2 with various connection conditions are calculated, as shown in Figure17. By comparing the load-displacement curve of calculation results of QX-2 with the experimental curve, it is shown that the load-displacement curve obtained by finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 17
Comparison of load-displacement curve for QX-2.


## 3.3.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QX-2 between the calculated results and the experimental results is shown in Table4.Table 4
Comparison of the ultimate bearing capacity and initial stiffness for QX-2.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results62.61.004.801.00Pure frame in finite element model70.61.132.620.55Two-point binding in finite element model109.91.765.561.16Surface binding in finite element model344.35.5020.294.23From Table4, it can be seen that the initial stiffness of the experimental specimen is 4.80 kN/mm, the bearing capacity is 62.6 kN, the frame model calculated initial stiffness is 2.62 kN/mm, and the bearing capacity is 70.6 kN. Wallboard can increase the rigidity of the structure. However, large concentrated stresses will be generated in the frame of the test specimen, which will cause premature failure of the weak points and reduce the bearing capacity of the structure. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 5.56 kN/mm and the bearing capacity is 109.9 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the QX-2 calculated model that is surface-bounded between the angle steel and the bent plate are 4.23 times and 5.50 times better than these of experimental results, respectively. It can be seen that increasing the connection strength of the wallboard in the experiment can strengthen the lateral restraint of the wallboard on the structure, especially for the columns in the middle of the frame.


## 3.4. Comparison of Calculation Results and Experimental Results for QY-1

### 3.4.1. Deformation

The load-displacement curves of the QY-1 with various connection conditions are calculated, as shown in Figure18. By comparing the load-displacement curve of calculation results of QY-1 with the experimental curve, it is shown that the load-displacement curve obtained by the finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 18
Comparison of load-displacement curve for QY-1.


### 3.4.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QY-1 between the calculated results and the experimental results is shown in Table5.Table 5
Comparison of the ultimate bearing capacity and initial stiffness for QY-1.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results52.61.007.151.00Pure frame in finite element model36.10.691.010.14Two-point binding in finite element model68.81.316.800.95Surface binding in finite element model445.28.4643.536.09From Table5, it can be seen that the initial stiffness of the experimental specimen is 7.15 kN/mm, the bearing capacity is 52.6 kN, the frame model calculated initial stiffness is 1.01 kN/mm, and the bearing capacity is 36.1 kN. It can be concluded that wallboard can increase the rigidity of the structure and also can ensure a certain degree of degeneration ability of the structure. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 6.80 kN/mm and the bearing capacity is 68.8 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the model in which the ends of the bent plate and the angle steel are connected by surface binding are higher than the experimental results. It shows that this type of connection has a significant effect on the overall performance of the structure, and the bent plate has a certain restraint effect on the vertical deformation frame.


## 3.4.1. Deformation

The load-displacement curves of the QY-1 with various connection conditions are calculated, as shown in Figure18. By comparing the load-displacement curve of calculation results of QY-1 with the experimental curve, it is shown that the load-displacement curve obtained by the finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 18
Comparison of load-displacement curve for QY-1.


## 3.4.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QY-1 between the calculated results and the experimental results is shown in Table5.Table 5
Comparison of the ultimate bearing capacity and initial stiffness for QY-1.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results52.61.007.151.00Pure frame in finite element model36.10.691.010.14Two-point binding in finite element model68.81.316.800.95Surface binding in finite element model445.28.4643.536.09From Table5, it can be seen that the initial stiffness of the experimental specimen is 7.15 kN/mm, the bearing capacity is 52.6 kN, the frame model calculated initial stiffness is 1.01 kN/mm, and the bearing capacity is 36.1 kN. It can be concluded that wallboard can increase the rigidity of the structure and also can ensure a certain degree of degeneration ability of the structure. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 6.80 kN/mm and the bearing capacity is 68.8 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the model in which the ends of the bent plate and the angle steel are connected by surface binding are higher than the experimental results. It shows that this type of connection has a significant effect on the overall performance of the structure, and the bent plate has a certain restraint effect on the vertical deformation frame.


## 3.5. Comparison of Calculation Results and Experimental Results for QY-2

### 3.5.1. Deformation

The load-displacement curves of the QY-2 with various connection conditions are calculated, as shown in Figure19. By comparing the load-displacement curve of calculation results of QY-2 with the experimental curve, it is shown that the load-displacement curve obtained by the finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 19
Comparison of load-displacement curve for QY-2.


### 3.5.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QY-2 between the calculated results and the experimental results is shown in Table6.Table 6
Comparison of the ultimate bearing capacity and initial stiffness for QY-2.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results65.41.008.301.00Pure frame in finite element model28.20.430.930.11Side contact of bending plate (0.06)497.87.6126.293.17Side contact of bending plate (0.15)517.97.9227.163.27Surface binding in finite element model611.99.3669.898.4250% surface binding in finite element model462.87.0846.416.0025% surface binding in finite element model372.55.7042.835.5912.5% surface binding in finite element model202.33.0925.453.07One-point binding in finite element model30.70.471.040.13Two-point binding in finite element model92.51.4113.811.66Single row node binding in finite element model330.35.0536.964.45Double-row node binding in finite element model744.611.3951.366.18From Table6, it can be seen that the initial stiffness of the experimental specimen is 8.30 kN/mm, the bearing capacity is 65.4 kN, the frame model calculated initial stiffness is 0.93 kN/mm, and the bearing capacity is 28.2 kN. That is to say, the wallboard significantly improves the stiffness of the structure by 8.9 times and bearing capacity by 2.3 times. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 13.81 kN/mm and the bearing capacity is 92.5 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the model in which the ends of the bent plate and the angle steel are connected by double-row node binding are higher than the experimental results. It can be seen that the stiffness of the actual component wallboard is not good enough, and the joint damage in the experiment greatly affects the stiffness and mechanical properties of the experimental specimen. It can be considered to increase the connection strength between the bent plates and between the bent plates and the frame to further improve the mechanical properties of the specimen.


## 3.5.1. Deformation

The load-displacement curves of the QY-2 with various connection conditions are calculated, as shown in Figure19. By comparing the load-displacement curve of calculation results of QY-2 with the experimental curve, it is shown that the load-displacement curve obtained by the finite element model with two-point binding between the end of the bent plate and the angle steel is closer to the experimental result.Figure 19
Comparison of load-displacement curve for QY-2.


## 3.5.2. Comparison of Bearing Capacity

Comparison of the ultimate bearing capacity and initial stiffness for QY-2 between the calculated results and the experimental results is shown in Table6.Table 6
Comparison of the ultimate bearing capacity and initial stiffness for QY-2.
Ultimate bearing capacity (kN)Increase multipleInitial stiffness (kN/mm)Increase multipleExperimental results65.41.008.301.00Pure frame in finite element model28.20.430.930.11Side contact of bending plate (0.06)497.87.6126.293.17Side contact of bending plate (0.15)517.97.9227.163.27Surface binding in finite element model611.99.3669.898.4250% surface binding in finite element model462.87.0846.416.0025% surface binding in finite element model372.55.7042.835.5912.5% surface binding in finite element model202.33.0925.453.07One-point binding in finite element model30.70.471.040.13Two-point binding in finite element model92.51.4113.811.66Single row node binding in finite element model330.35.0536.964.45Double-row node binding in finite element model744.611.3951.366.18From Table6, it can be seen that the initial stiffness of the experimental specimen is 8.30 kN/mm, the bearing capacity is 65.4 kN, the frame model calculated initial stiffness is 0.93 kN/mm, and the bearing capacity is 28.2 kN. That is to say, the wallboard significantly improves the stiffness of the structure by 8.9 times and bearing capacity by 2.3 times. The initial stiffness of the analysis model with two-point binding connection between the bent plate and the angle steel is 13.81 kN/mm and the bearing capacity is 92.5 kN, which are relatively close to the initial stiffness and bearing capacity of the experimental specimen. The initial stiffness and bearing capacity of the model in which the ends of the bent plate and the angle steel are connected by double-row node binding are higher than the experimental results. It can be seen that the stiffness of the actual component wallboard is not good enough, and the joint damage in the experiment greatly affects the stiffness and mechanical properties of the experimental specimen. It can be considered to increase the connection strength between the bent plates and between the bent plates and the frame to further improve the mechanical properties of the specimen.


## 4. Conclusions

Experimental analysis and finite element analysis are carried out on different structural forms of modular wallboards structure. The load-displacement curves, bearing capacity, and stiffness calculated by the finite element analysis are compared with the experimental results. The following conclusions can be drawn:(1)
The calculation result of finite element analysis is slightly higher than the experimental value, which is considered to be caused by the initial defects of the specimens not considered in the finite element analysis. In the elastic phase, the load-displacement curve calculated by finite element analysis is in good agreement with the experimental results, which can verify that the finite element model and analysis methods are correct and effective.(2)
It can be obtained that the simulation results of the finite element model with the two-point binding connection between the bent plate and the angle steel are in good agreement with the experimental results. The finite element model established by two-point binding constraints is more suitable for practical engineering.(3)
For QX-1 and QX-2, the initial stiffness and bearing capacity of the structure with surface-bound between the bending plate and the angle steel have a significant effect on the improvement of the experimental results. The initial stiffness and bearing capacity of the QY-2 model when considering surface binding and double-row node binding are also greatly improved. Therefore, it can be considered to increase the connection strength between the bent plates and between the bent plates and the frame to further improve the mechanical properties of the specimen.



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*Source: 7299626-2022-04-14.xml*