# Bearing Behavior of Cold-Formed Thick-Walled Steel Plates with a Single Bolt
## 4 Discussion
### Comparison of Failure Modes  
In the standard of ANSI/AASC 360-22 [6], ultimate capacities can be calculated using Equations (1)-(3) for specimens with the failure modes of a net-section rupture, as well as bearing and shear-out phenomena. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimen** & **Failure Mode** & \(F_{\mathbf{u}}\) **(kN)** & \(F_{\mathbf{u}}\)/\(f_{\mathbf{u}}\)/\(d_{t}\) & \(F_{\mathbf{u}}\)/\(f_{\mathbf{u}}\)/\(A_{\mathbf{net}}\) & \(\delta_{\mathbf{u}}\) **(mm)** \\ \hline D6.0-1.5-1.0 & Net-section fracture & 71.5 & \(-\) & 0.95 & 3.24 \\ D6.0-1.5-1.2 & Net-section fracture & 94.5 & \(-\) & 1.05 & 3.98 \\ D6.0-1.5-1.5 & Shear-out & 104.0 & 1.73 & \(-\) & 7.79 \\ D6.0-1.5-2.0 & Shear-out & 102.0 & 1.69 & \(-\) & 6.71 \\ D6.0-1.5-3.0 & Shear-out & 102.0 & 1.69 & \(-\) & 6.98 \\ D10.0-1.5-1.0 & Net-section fracture & 130.7 & \(-\) & 0.96 & 3.10 \\ D10.0-1.5-1.2 & Net-section fracture & 154.2 & \(-\) & 0.94 & 4.37 \\ D10.0-1.5-1.5 & Shear-out & 176.7 & 1.62 & \(-\) & 7.19 \\ D10.0-1.5-2.0 & Shear-out & 182.2 & 1.67 & \(-\) & 6.88 \\ D10.0-1.5-3.0 & Shear-out & 186.2 & 1.71 & \(-\) & 6.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Test results for specimens with varying edge distances. Figure 8: Curves of relationship between (normalized) ultimate strength and normalized end distance. Figure 9: Curves of the relationship between ultimate strength and normalized edge distance. \[R_{n}=f_{u}A_{e}=(2e_{2}-d_{0})f_{u}t \tag{1}\]  
\[R_{b}=3.0 dtf_{u} \tag{2}\]  
\[R_{s}=1.5l_{c}tf_{u}=1.5(e_{1}-0.5d_{0})tf_{u} \tag{3}\]  
Here, \(f_{u}\) is the tensile strength of the connected plates, \(A_{e}\) is the net area subject to tension, \(t\) is the base steel thickness of a section, \(d\) is the bolt diameter, and \(l_{c}\) is the clear distance in the direction of the force. A bearing failure happens when \(R_{b}<R_{s}\) and \(R_{b}<R_{n}\). From Equations (1)-(3), it can be obtained that a bearing failure occurs when \(e_{1}>2d+0.5d_{0}\) and \(e_{2}>1.5d+0.5d_{0}\). Similarly, a shear-out failure occurs when \(e_{1}<2d+0.5d_{0}\) and \(e_{2}>0.75e_{1}+0.125d_{0}\), and a net-section fracture occurs when \(e_{2}<\min\) [\(1.5d+0.5d_{0}\), \(0.75e_{1}+0.125d_{0}\)]. When Equation (3) is used to calculate the ultimate capacity of a shear-out failure, assumptions are made that the steel plates fail along the centerlines of the bolt holes in the loading direction and that the limiting stress along the shear failure planes is \(0.75f_{u}\). However, it is impossible that the shear failure plane coincides with the centerline of the bolt holes in the loading direction because the shear stress on this plane is zero when the bearing stress in front of the bolt is symmetrically distributed. This has been confirmed by the results of the finite element analysis of [19], the experimental observations of [20], and our tests. Therefore, [PERSON] et al. [21] proposed a definition of the effective shear planes, which were the midways between the net and gross shear planes, and they were assumed to be the shear failure planes. Additionally, the maximum stress was assumed to be \(0.60f_{u}\) on the effective shear planes. Based on the studies of [PERSON] et al. [21], the ultimate capacity of shear-out failures can be calculated using the following equation:  
\[R_{s,m}=1.2l_{e}tf_{u}=1.2(e_{1}-0.25d_{0})tf_{u} \tag{4}\]  
where; \(l_{e}\) is the effective shear length, which is the mean value of the net shear length (\(e_{1}-0.5d_{0}\)) and the gross shear length (\(e_{1}\)). Figure 9 presents the conditions of the end/edge distance combinations for different failure modes specified in the design code of ANSI/AASC 360-22 [6]. According to Equations (1), (2) and (4), the conditions of the end/edge distance combinations can be obtained for specimens failed by bearing, shear-out, and net-section fractures, as shown in Figure 9.  
Figure 10: Conditions of end/edge distance combinations of different failure modes according to ANSI/AASC 360-22 [6] before and after modification.