# Axial and Bending Bearing Capacity of Double-Steel-Concrete Composite Shear Walls
## 3 Numerical Analysis  
### FE Model  
In the structure of SC walls, the concrete is covered by the surface steel plates, so it is difficult to measure the ultimate compressive strain of the concrete and the average strain. In this paper, the finite element analysis was done using ABAQUS (Dassault Systemes, Providence, Rhode Island, USA, 2010) to obtain the strain distribution of the concrete, to verify the plane assumption, and to carry out the parametric analysis. There are few experiments on small eccentric compression failure, so the SC walls having small eccentric compression failure were simulated by ABAQUS. Nonlinear finite element analysis was performed on all samples in [12] using ABAQUS. The reinforcement diagram of a specimen is shown as an example in Figure 1. The upper and lower parts of the SC wall were embedded in the loading beam and the base beam, respectively, for applying the lateral load and anchoring with the foundation. The parameters of specimens are shown in Table 2. Studs were set on the inner surface of the steel plate and tie bars were arranged between the steel plates. In the test, the specimen was fixed on the ground by two long bolts. The concrete grade was C35. The average cube compressive strength was 42.9 MPa, and the Young's modulus was 33,000 MPa. The average yield strength of the steel plate was 330 MPa, and the Young's modulus was 206 GPa. The quasi-static method was applied in the loading test. First, the vertical load was applied to the specimen until the design axial compression ratio was achieved. Then a lateral load was applied on the top of the wall. Before yielding, the lateral load increased step by step according to 1/10 of the ultimate load, which was estimated, and one cyclic loading was performed at each step. The design axial compression ratio (\(\mu\)) refers to the ratio of the representative value of the load to the design value of the material strength, which can be expressed as follow:  
\[\mu=\frac{N}{f_{c}A_{c}+f_{y}A_{s}} \tag{1}\]  
where \(N\) is the design value of the axial pressure of the specimen under the action of the representative value of the gravity load. \(f_{c}\) is the design value of concrete compressive strength. \(f_{y}\) is the design value of the yield strength of the steel plate. \(A_{c}\) and \(A_{s}\) are the concrete cross section area and the steel plate cross section area, respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multicolumn{3}{c}{**Specimen Size**} & **Steel Plane** & **Design Axial** & **Stud** \\ \cline{2-7}  & **Height** & **Width** & **Thickness** & **Thickness** & **Compression Ratio** & **Spacing** \\ \hline SCW1-1a & 1000 & 1000 & 150 & 3 & 0.4 & 40 \\ SCW1-1b & 1000 & 1000 & 150 & 3 & 0.4 & 40 \\ SCW1-2a & 1500 & 1000 & 150 & 3 & 0.4 & 40 \\ SCW1-2b & 1500 & 1000 & 150 & 3 & 0.4 & 40 \\ SCW1-3 & 2000 & 1000 & 150 & 3 & 0.4 & 40 \\ SCW1-4 & 1000 & 1000 & 150 & 2 & 0.4 & 40 \\ SCW1-5 & 1000 & 1000 & 150 & 4 & 0.4 & 40 \\ SCW1-6 & 1000 & 1000 & 150 & 3 & 0.4 & 80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameters of specimens. The ABAQUS model of specimens taken from [12] is shown in Figure 2. The concrete was modeled with the C3D8R solid element; the steel plate was modeled with the S4R shell element; the tie bar was modeled with the T3D2 truss element, which is similar to [27]. The stud was modeled with the SPRING2 element. In this paper, a three-way zero-length spring was added between the concrete slab node and the steel plate node at the actual position of the stud. The spring stiffness includes shear stiffness and axial stiffness. Aiming at the shear-slip curve, [PERSON] et al. [28] proposed a calculation model, which has been widely recognized. The shear-slip curve is expressed as:  
\[V=V_{u}(1-e^{-ns})^{m} \tag{2}\]  
where \(s\) is the slippage. \(m\) and \(n\) are parameters. Different researchers used Equation (2) to fit the \(m\) and \(n\) according to their test results.