## 4 Proposed Method for Calculating Nominal Strength of an Integrated Panel with Reinforced Studs  
### Draft Prediction Equation for the Nominal Strength of an Integrated Panel with Reinforced Studs  
To predict the nominal strength of the integrated panel, it is assumed that the integrated panel is composed of studs and steel sheets like in a steel-sheathed wall system. [PERSON] and [PERSON] [30] developed an analytical design method--known as the effective strip method--to predict the nominal strength of CFS-framed shear walls with steel sheet sheathing. This method uses the minimum strength of the screw connections to the effective strip and the effective width strength of the tension strip to determine the nominal strength of the wall system, after assuming the effective width according to the specifications of the steel-sheathed wall. Therefore, a sheet-sheathed wall system can be designed similar to a steel strap brace wall system. However, since the integrated panel is produced by bending one steel sheet, it is difficult to assume the effective width, because there are no screw joints. To solve this problem, we refer to the study by [PERSON] et al. [25], who tested and analyzed cold-formed steel strap-brace shear walls, and suggested that frame action should be considered in addition to truss action by strap braces. Figure 13: Variation in the stress at the section measured using strain gauges attached to the vertical direction at a height of 400 mm with the drift ratio of the IP specimen. When a lateral force is applied to the IP, the force mechanism acting within the integrated member can be expressed as a frame action and a truss action, as shown in Figure 14. \(V_{f}\) and \(V_{t}\) are the lateral forces in the frame and truss actions, respectively. When considering frame action independently, there is no steel sheet (from the steel-sheathed wall system) in the integrated member. Thus, knowing the lateral stiffness, \(k_{f}\), and the yield displacement, \(\delta_{y}\), \(V_{f}\) can be calculated as follows:  
\[V_{f}=\delta_{y}k_{f}=\delta_{y}\left[2\cdot\frac{12E\left(I_{f}C\right)}{h^{3 }}\right] \tag{5}\]  
where \(E\) is the elastic modulus, \(I_{f}\) is the moment of inertia of the flange portion of the integrated member with reinforced studs (see effective section of vertical member in Figure 14), \(C\) is a coefficient that helps reflect a change in the effective moment of inertia when a load is applied (as mentioned in Section 4.2, \(C\) is 0.09 and 0.24 for the inner and outer stud-reinforced integrated panels, respectively), and \(h\) is the height of the integrated member. Using the calculated \(V_{f}\), the bending moment acting on the stud--\(M_{base}\) and \(M_{hold-down}\) in Figure 14--can be evaluated as  
\[M_{base}=\frac{V_{f}h}{4} \tag{6}\]  
\[M_{hold-down}=M_{base}\left(\frac{0.5h-h_{o}}{0.5h}\right) \tag{7}\]  
The truss action assumes the behavior of the integrated member equal to the steel strap-braced wall system or the effective strip method of steel-sheathed wall system. In truss action, tension is applied to the strip, and the resulting compressive force acts on the flange portion of the integrated member. As the effective width of strip is unknown, the bending moment acting on the stud must be used to predict the compressive force acting on the stud. According to AISI S100, the maximum allowable compressive force acting on the flange portion of the integrated member \(\overline{P}_{r,max}\) can be evaluated as follows:  
\[\overline{P}_{r,max}=P_{no}\left(1-\frac{\overline{M}_{ry}}{M_{ny}}\right) \tag{8}\]  
where \(P_{no}\) represents the nominal capacity term for axial compression, \(\overline{M}_{ry}\) is the required flexural demand about the \(y\)-axis such that \(\overline{M}_{ry}=M_{h}\), and \(M_{ny}\) is the nominal bending capacity about the \(y\)-axis.