Study on Seismic Performance of Cold-Formed Thin-Walled Steel-Straw Board Composite Wall with Diagonal Brace

: The composite wall studied in this paper is based on the original cold-formed thin-walled steel-straw board composite wall, which is set up with inclined braces and rigid inclined braces to improve its seismic performance. The factors of aspect ratio are analyzed, and the formula of shear bearing capacity of composite wall is deduced. The results show that: (1) When the height-width ratio of the composite wall is 2.4m×1.2m, 1.8m×1.2m and 1.2m×1.2m respectively, the yield strength of the composite wall is 35.78kN, 37.47kN and 54.23kN respectively. The yield strength of the former increases by 4.72 %, and the yield strength of the latter increases by 44.73 %. (2) Using the effective strip method, the error of the derived shear capacity formula is not large, and the difference between the experimental value and the simulated value is not large, in order to provide some reference for the seismic design of this kind of cold-formed thin-walled steel-strawboard composite wall with diagonal brace.


Introduction
Gao Wancheng [3] summarized the shear test results of cold-formed thin-walled steel walls at home and abroad, and gave the influence of wall panel type, wall height-width ratio, opening and loading mode on the shear capacity of the wall.In terms of numerical simulation: Nie Shaofeng [8,9] derived the calculation method of the shear capacity of the wall by using the overall analysis method and the shear flow method respectively, and the calculation formula is biased towards safety.Niari [1] used ABAQUS software to simulate the wall of thin steel plate.In the model, all components were simulated by shell elements, and the self-tapping screws were simulated by nonlinear connection elements.The contact between the components was considered and the geometric nonlinearity was turned on.
Based on the previous research, ABAQUS is used to analyze the influence of the change of height-width ratio parameters on the seismic performance of the composite wall with diagonal bracing under horizontal monotonic load, and a simplified model of wall bearing capacity is established to derive the formula, which provides a theoretical reference for such engineering applications.

Establishment of finite element model 2.1 ABAQUS selection
This section will introduce the finite element analysis software ABAQUS6.14 in detail, and establish a new type of cold-formed thin-walled steel composite wall with diagonal brace.

Model unit selection and meshing
The light steel keel consists of steel column, diagonal brace, upper guide rail and lower guide rail connected by self-tapping screws.Q235 galvanized cold-formed thin-walled C steel is used for the steel column and diagonal bracing of the light steel keel.The specifications are C90x40x15x1mm (web height x flange width x curling width x section thickness).Because the side column of the wall specimen is subjected to a large force under the action of earthquake, the side column is connected by two back-to-back C-shaped steel columns through self-tapping screws; the middle column is located in the middle of the wall; the self-tapping screw used in the production process of light steel keel is ST3.5x75 mm plum blossom countersunk head self-tapping screw; the upper and lower guide rails adopt Q235 galvanized cold-formed thin-walled U-shaped steel with a specification of U93x45x1.5mm(web height x flange width x cross-section thickness), and are connected to the top beam and the bottom beam through M18 high-strength 10.9 bolts.The section of the keel column and the guide rail is shown in Figure 1.

Simulation method of self-tapping screw connection
The simulation of the self-tapping screw is based on the Cartesian and aline connectors in Basic to simulate the connection of the self-tapping screw between the straw board and the light steel skeleton, as shown in Figures 2  and 3.

Model validation in this paper
The finite element analysis software ABAQUS is used to simulate and analyze the sdwgc cold-formed thin-walled steel wall in reference [12] .The finite element analysis and test results are compared and verified from three aspects: failure mode, skeleton curve and eigenvalue.

Comparison of failure modes
The specimen is a composite wall specimen without internal bracing.During the loading process, local buckling occurs at the bottom of the side column, and the wrinkles of the straw board are mainly concentrated around the wallboard.Figure 6 is the finite element failure mode, which is basically consistent with the failure phenomenon of the reference test.

Comparison of skeleton curves
The skeleton curve [11] refers to the curve formed by connecting the peak points reached in each displacement cycle from the initial point of loading.The curve can reflect the stress and ductility of the member at different stages.The comparison results are shown in Figure 7.It can be seen from Fig. 7 that the skeleton curves are in good agreement, but the peak load of the finite element simulation is slightly higher than the peak load of the test.Because the finite element simulation model is a simplified model, the results are not completely consistent.

Comparison of eigenvalues
From the skeleton curve of the model, the yield displacement, yield load and peak load of the model can be analyzed.In this paper, the Park method is used, see figure 8.In addition, the maximum load max P and maximum displacement max of the specimen correspond to the peak point in the skeleton curve, and the data are shown in Table 1.It can be seen from Table 2, the error between the finite element and the test is small and the agreement is good, indicating that the finite element model is reasonable and can be used for further parameter analysis.

Finite element analysis of seismic performance of composite wall
On the basis of verifying the model, Abaqus was used to change the support mode in the wall, and the influence of relevant parameters on the seismic performance of the composite wall was analyzed, and the characteristic values of bearing capacity were compared.It is found that the seismic performance of the composite wall with diagonal brace is better than the former two.

Analysis of the influence of support mode
The It can be seen from Fig. 9 that the composite wall with inclined support can make full use of the steel performance before the end of loading, and the stress is concentrated in the middle of the support of the composite wall.The skeleton curve can reflect the yield displacement, yield load, peak point and ductility coefficient of the component.The calculation of ductility is in accordance with the provisions of the " Building Seismic Test Procedures " [11] , and the ductility coefficient is used to represent the ductility.The calculation formula is shown in (1).In the formula, the ultimate displacement needs to be determined, and the ultimate displacement is specified as the displacement corresponding to 0.85 max P in the descending section of the skeleton curve.(1)

Skeleton curve and its eigenvalue comparison
In the formula: u  is the ultimate displacement of the specimen; y  is the peak displacement corresponding to the peak load of the specimen.
The skeleton curve of the composite wall is shown in Fig. 10, and the corresponding seismic bearing capacity characteristic value is shown in Table 3.According to the relevant regulations, when the ductility coefficient is less than or equal to 1.5, the deformation capacity of the specimen is considered to be weak.When the ductility coefficient is greater than 3.5, it is considered that the deformation capacity of the specimen is superior; when the deformation coefficient is in the middle value, the deformation ability of the specimen is considered to be medium.The results show that the seismic performance of the supported model is better than that of the original model, and the improvement of the internal bracing is the most obvious.The yield load, peak load and continuation coefficient are increased by 94.14%, 88.84% and 64.19% respectively, indicating that the composite wall with rigid bracing can effectively improve the seismic performance.

Comparison of failure modes
The parameter analysis of the composite wall is carried out by numerical simulation, and the influence of changing the aspect ratio on the bearing capacity of the composite wall is considered.The parameters of each reference are shown in Table 4.After the finite element simulation analysis, the stress cloud diagram of each component of the composite wall can be seen in figure 11 through post-processing.It can be seen from Fig. 11 that the columns and braces of the composite wall are buckling, and the most serious is the 2.4m×1.2mcomposite wall.It can be seen from the figure that the stress of the braces and columns decreases with the decrease of the height-span ratio, that is, the damage of the composite wall is weakened.This is because most of the force of the composite wall is borne by the skeleton and brace of the composite wall.It can be seen from Fig. 12 and Table 5 that reducing the height-span ratio can improve the seismic performance of the composite wall, because it can improve the comprehensive force of the column and the diagonal brace and reduce the overall deformation of the composite wall.

Calculation formula of shear bearing capacity of composite wall
The theoretical formula of shear bearing capacity of cold-formed thin-walled steel-strawboard composite wall with diagonal brace is derived.In order to understand the failure mode of composite wall, the corresponding balance formula is established based on the failure model of wall, so as to obtain the calculation method of bearing capacity.

Effective Strip Method
Summarizing the domestic and foreign literature [14,4,2,5,7,10] , it is concluded that the failure modes of the composite wall mainly include the following situations : shear failure of the self-tapping screw, failure of the self-tapping screw to pull out the covering panel, failure of the wall panel, buckling failure of the diagonal brace, etc.According to the North American AISI specification, the formula for calculating the strength of screw connections is as follows: (1) When    ( )  The relationship between the arrangement of screws and the maximum effective width is shown in Fig. 15.

Comparison of finite element simulation results and overall analysis results
The calculated value of the shear bearing capacity of the composite wall derived by the effective strip method is compared with the finite element simulation results.The data of three different composite walls with diagonal bracings with wall sizes of 2.4m×1.2m,1.8m×1.2mand 1.2m×1.2mwere compared with the shear bearing capacity formula derived from the effective strip method abroad, and then summarized and analyzed.
Comparison process: (1) The finite element simulation data of composite wall with diagonal bracings with wall size of 2.4m×1.2mare compared with the effective strip method formula.
The shear bearing capacity of the composite wall is derived from the strength value of the self-tapping screw connection: Therefore, the smaller value between the two, that is, 31.97KN, is taken as the shear capacity of the composite wall.
(2) The finite element simulation data of 1.8m × 1.2m composite wall with diagonal bracing are compared with the formula of effective strip method.
Similar to the above solution process, not too much calculation is done here, only the calculation results are given.
The shear bearing capacity of the composite wall is derived from the strength value of the self-tapping screw connection: The shear bearing capacity of the composite wall is deduced from the tensile strength value of the straw board: 9 cos 6 .97Therefore, the smaller value between the two, that is, 38.27KN, is taken as the shear capacity of the composite wall.
(3) The finite element simulation data of 1.2m×1.2mcomposite wall with diagonal bracing are compared with the formula of effective strip method.
Similar to the above solution process, not too much calculation is done here, only the calculation results are given.
The shear bearing capacity of the composite wall is derived from the strength value of the self-tapping screw connection: The shear bearing capacity of the composite wall is deduced from the tensile strength value of the straw board:  It can be seen from Table 6 that the minimum error between the theoretical calculation results and the test results is 0.99 %, and the maximum is 10.66 %.It shows that the formula derived from the effective strip method is reasonable and can provide reference for engineering design.

The experimental results are compared with the results of the effective strip method.
In order to further verify the correctness of the shear bearing capacity formula of the composite wall derived by the effective strip method, this paper not only quotes the data in Zhang Enyuan 's [13] paper, that is, Sddg1.0ic and Sdsg1.0ictest data, but also quotes the data of Ling Ligai 's [6] paper, that is, wsS-so75-0.75-1specimen data.The parameters are substituted into the shear capacity formula of the composite wall derived by the effective strip method, and the comparison results are shown in table 7. It can be seen from Table 7 that the error is controlled within 15%, which is in good agreement.The surface test value can also be in good agreement with the shear capacity formula of the composite wall derived from the effective strip method, which further verifies the correctness and wide applicability of the effective strip method.

Conclusion
In order to be better applied to the composite wall, the finite element simulation analysis and theoretical derivation analysis of the seismic performance of the cold-formed thin-walled steel-straw board composite wall with diagonal bracing are carried out in this paper.The influence factors of height-width ratio on the bearing capacity of composite wall under low cyclic horizontal load were studied.The effective slice method for calculating the shear capacity of composite walls is introduced, and its correctness and wide applicability are verified.Based on this, the following conclusions can be drawn: (1) Based on the test results of the existing literature, the finite element analysis of the cold-formed thin-walled steel-strawboard composite wall with diagonal braces under low-cycle reciprocating horizontal loading was carried out by using ABAQUS software.The results show that the error between the maximum load value of the experiment and the maximum load value of the finite element simulation is 2.10 %, the error of the yield load is 2.49 %, and the error of the yield displacement is 8.90 %.It can be seen that the finite element simulation values are in good agreement with the experimental values, which verifies the correctness and rationality of the finite element model.
(2) When the aspect ratio of the composite wall is 2.4m×1.2m,1.8m×1.2mand 1.2m×1.2mrespectively, the yield strength of the former increases by 4.72%, and the yield strength of the latter increases by 44.73%.
(3) Through the parameter analysis of the finite element model, it can be seen that the aspect ratio will affect the bearing capacity of the wall.Reducing the aspect ratio can improve the bearing capacity of the wall, but the aspect ratio should not be less than 1.
(4) In this paper, the effective strip method is used to derive the calculation formula of the shear capacity of the composite wall.The minimum error between the theoretical calculation result and the test result is 0.99 %, and the maximum is 10.66 %.The subsequent comparison can be well consistent with the test value and the simulated value.

Figure 1
Figure 1 Cross-section of keel column and guide rail

Figure 4 Figure 5
Figure 4 Coupling relationship between top beam web and reference point RP-1

Figure 6
Figure 6 Finite element failure pattern

Figure 7
Figure 7 Simulated skeleton curve and experimental comparison chart

Figure 8
Figure 8 Park method to determine the yield point.

Figure 9
Figure 9 Varying stress cloud diagram of different support methods

Figure 10
Figure 10 Comparison diagram of skeleton curve of wall with different support methods

7 E3SFigure 11
Figure 11 Stress cloud diagram of different aspect ratio composite wall

Figure 12
Figure 12 Comparison diagram of skeleton curve of different height and width ratio composite walls

2 t-
The thickness of light steel skeleton; d -The diameter of the screw; 1 u F -the tensile strength of the cladding panel; 2 u F -Tensile strength of light steel skeleton.Foreign scholars deduced the calculation formula of shear capacity of composite wall with thin steel plate by effective strip method, and the stress model is shown in Fig.13.n n V T  =  , of which n T is determined by the minimum value of the connection strength of the screw and the bearing capacity of the wall panel, that is, the following formula : minimum value of the screw connection strength is obtained from Eqs. (2) -(6).The force analysis of the screw is shown in Fig.14.T -Steel plate thickness; y F -Yield load of steel plate; e W -Effective band width.
connection strength between the wall panel and the top and bottom guide beams; , ns s P -The connection strength between wall panel and wall frame column; , ns t s P  -The connection strength between the wall panel and the guide beam and the wall column.

Figure 13 Figure 14 Figure 15
Figure13 Force analysis diagram of effective strip method model

3 .
Screw shear strength value calculationAccording to the simulation data, it can be seen that the strength of the screw connection is determined by the light steel skeleton.The strength of the screw connection is 4.467KN calculated by the formula.Get: , , , Therefore, the smaller value between the two, that is, 53.70KN, is taken as the shear capacity of the composite wall.

Table 1
Parameters of each component of the internal non-diagonal brace composite wall

Table 2
Comparison of finite element and test eigenvalues

Table 3
Comparison of bearing capacity characteristic values of walls with different support methods

Table 4
Parameters of each datum under different height and width ratio composite walls

Table 5
Comparison of seismic bearing capacity characteristic values of different aspect ratio composite walls

Table 6
Comparison of simulation results and theoretical calculation results of composite walls with different high span ratios

Table 7
Comparison of test results and theoretical calculation results