# Analytical Method

A review of various analytical approaches that can be relied on to determine the strength and deflection of wood framed shear walls has been presented by Chen (2004). These models were used to predict the lateral load capacity, which was defined as the yield shear strength, Sy, and the corresponding deflection of the wall Anet, y (Fig. 2). In this paper a summary of a strength and deflection model is presented. Figure 4 shows the assumed deformations and force distribution of a typical light gauge steel frame / wood panel shear wall. The lateral load at the top of the wall produces a moment and a horizontal force on the wall bottom. If the hold-downs are designed to fully transfer the tension force into the support through the end studs, the vertical forces acting on the end studs are balanced by the shear flow along the screw lines on the end studs, which is produced by sheathing rotation relative to the steel frame. The shear flow causes the axial forces in the end studs to distribute triangularly, with the maximum forces at the bottom of the end studs (Stewart, 1987). With respect to the top track, if the screw spacing along the top edge of the sheathing and the spacing for anchors to the load beam are both small enough to assume the applied force is uniform, then no axial force exists. Similar for the bottom track, the applied force can be considered uniform if the screw and shear anchor spacing is small. The interior studs at the centreline of a panel or at the joint of two panels with the same width are assumed to carry no axial forces due to lateral loads causing in-plane shearing of the wall. The interior studs also provide out-of-plane support to stiffen the sheathing panel against shear buckling. The studs at the panel joints act as splices between adjacent wood panels; hence the design of the back-to-back studs needs to incorporate the shear force due to the opposite rotation of the two adjacent panels. Triangularly distributed forces also act perpendicular to the axes of the studs and tracks attached to the edges of panels, due to the relative displacements between studs and panels. In a capacity based design approach the size of the steel frame members is selected such that the frame itself does not fail. Given this information, and for simplification purposes, the frame members can be assumed to be rigid in the analytical models.