# Finite Element Analysis

3.1. Finite Element Analysis Model

Finite element analysis model was a mathematic representation of the practical structure, and the model and method of analysis should reflect the main performance of every member. The balanced equation of wall was listed as follows

[K]{5} = [P], (1)

where [K] is the stiffness matrix of structure ([K] = fV[B]r[D][B] dV), [B] stands for the geometric matrix, [D] stands for the material constitutive matrix, and V stands for the structure volume, {5} is the joint displacement vector and [P] is the load vector.

{a} = [D]{e}, (2)

M = [B]{5}, (3)

where {a} is the stress matrix and {e} is the stain matrix.

The stiffness matrix of structure [K] was not constant because the balanced equation considered the geometric and materials nonlinearity. Both the matrices [D] and [B] were related to the stress or strain.

Table 3. Material properties of specimen.

 Material Young’s modulus (N/mm2) Tensile strength (N/mm2) Poisson’s ratio Gypsum 1124.7 0.66 0.23 OSB 3500 7.86 0.3 Steel 2.06e5 320 0.3

 Fig. 6. Finite element models of wall.

The finite element analysis program ANSYS was used to analysis the wall specimens under the monotonic load. The plastic shell elements “shell 181” were used to simulate the cold-formed steel members and sheathing panels. The material properties referring to Kasal et al. (1992), Thomas (2002) and Zhou et al. (2004) are listed in Table 3. The screw connections were handled by coupling method, and the screws were assumed to have free rotations but no displacement along the X, Y and Z-directions without considering the slip between sheathing and steel members. The studs and tracks were simply connected. The displacements along the X, Y and Z-directions and rotations along Y and Z-directions of bottom track were restrained, which means Ux = 0, Uy = 0, Uz = 0, ey = 0 and ez = 0. And the top track was assumed to have no displacement and rotation along the Y and Z-directions, or Uy = 0, Uz = 0, 0y = 0 and 9z = 0. The finite element model is illustrated in Figure 6. The nodes of top track were coupled in X-directions, and the displacement corresponding to the maximum load was applied on the coupled node. The loading process was controlled by displacement load.