For the injector faceplate to stay fastened to the manifold, the bolts must satisfy a factor of safety for both tensile and shear stress. A net upward pressure acting on the faceplate applied to the area of the injector requires all bolts on the injector manifold -both axial and radial- to withstand this force to maintain structural integrity.
Hot Fire Calculations:
\[ \begin{align*}
& F_{up} = P_{injector}*A_{injector} \\
& F_{up} + N*F_{bolt}=0 \\
& \\
&|F_{bolt}| = \frac{P_{injector}*A_{injector}}{N} \\
& Stress_{Tensile}: σ = \frac{|F_{bolt}|}{A_{bolt}} = \frac{P_{injector}*A_{injector}}{N*A_{bolt}} \\
\end{align*}
\]