## 2 Load on Silo Hotspot Detector
### Normal Pressures on Vertical Wall  
To find the tensile force applied to the product in the vertical wall section, pressure \(P_{hf}\) applied to the vertical wall (Figure 1) must be obtained. \(P_{hf}\) can be obtained as  
\[P_{hf}(z)=P_{ho}Y_{f}(z) \tag{1}\]  
where \(z\) is the depth from the load equivalent surface, \(Y_{f}(z)\) is the Janssen function, and \(P_{ho}\) is the pressure when \(z=z_{o}\). Furthermore, \(z_{o}\) indicates the specific depth at which the pressure becomes  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multicolumn{2}{c}{**Unit Weight**} & \multicolumn{2}{c}{**Internal Friction Degree**} & \multicolumn{2}{c}{**Lateral Pressure Ratio**} & \multicolumn{2}{c}{**Wall Friction**} \\  & (\(\gamma\), kN/\(m^{3}\)) & \multicolumn{2}{c}{(\(\phi_{\mu}\), _degree_)**} & \multicolumn{2}{c}{(K)} & \multicolumn{2}{c}{(\(\mu\))} \\ \hline \multirow{3}{*}{Coal} & \(\gamma_{l}\) & \(\gamma_{u}\) & \(\phi_{im}\) & \(a_{\phi}\) & \(K_{m}\) & \(a_{K}\) & \(D2\) & \(a_{\mu}\) \\  & Lower & Upper & Mean & Factor & Mean & Factor & Mean & Factor \\ \cline{1-1}  & 7.0 & 10.0 & 31 & 1.16 & 0.52 & 1.15 & 0.49 & 1.12 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties.  
Figure 1: Target silo shape and specification.  
stable. To determine the maximum pressure generated, it is necessary to assume that the silo is full and extreme. In addition, in order to consider maximum normal pressures on the vertical wall with reference to Eurocode, a friction coefficient \(\mu\) is the minimum value (lower limit value), a lateral pressure ratio \(K\) is the maximum value (upper value), and an internal friction angle angle \(\_\phi_{i}\) with a minimum value (lower limit value).  
Lower characteristic value of \(\mu=\frac{\mu_{m}}{a_{\mu}}\)  
Upper characteristic value of \(K=a_{K}K_{m}\)  
Lower characteristic value of \(\phi_{i}=\frac{\phi_{im}}{a_{\phi}}\)  
Through the above values, the pressure \(P_{hf}(z)\) applied normally to the vertical wall of the target silo according to depth \(z\) can be obtained. However, this study aimed to find the tensile force generated in the product by the outflow, and therefore, the outflow coefficient \(C_{h}\) for the horizontal pressure was considered. The discharge coefficient \(C_{h}\) is a factor that considers many phenomena that occur when the silo load is discharged, and it is determined by classification based on the capacity of the silo. It can be confirmed that the target silo is classified as AAC 2 [23] and has a value of a discharge factor for a horizontal pressure \(C_{h}=1.15\). Therefore, the pressure acting perpendicular to the silo wall by the outflow is given by  
\[P_{hf}(z)\times C_{h}=1.15P_{hf}(z) \tag{2}\]  
This pressure acts equally on the product. Therefore, to determine the tensile force applied to the detector, \(1.15\)\(P_{hf}(z)\) is integrated by the outflow against depth \(z\) and the coefficient of friction is multiplied by the circumference of the product. The integral value for \(z\) is  
\[\int_{0}^{z}1.15\,P_{hf}(z)dz=1.15P_{h0}\Big{[}z-z_{o}Y_{J}(z)\Big{]}. \tag{3}\]  
Multiplying this value by the coefficient of friction \(\mu\) and the circumference of the detector gives the tensile force acting on the detector by the silo vertical wall section.