$8\mathrm{.}33$ Figure P$8\mathrm{.}33$ shows a cantilever beam serving as a spring for a latching mechanism. When assembled, the free end is deflected $0\mathrm{.}075$ in $.,$ which corresponds to a force $\backslash ($ F $\backslash )$ of $8\mathrm{.}65$ lb $.$ When the latch operates, the end deflects an additional $0\mathrm{.}15$ in $.$ Would you expect eventual fatigue failure?

$[$Ans$.$: It is marginal.$]$

Estimate $\backslash (\backslash$mathrm$\{$Sn$\}^\{\backslash$prime$\}=100\backslash )$ based on Figure $8\mathrm{.}6$ and that $\backslash ($ S n$^\{\backslash$prime$\}=0\mathrm{.}25\backslash )$ Bhn only for Bhn up to $\backslash (\backslash$sim $400\backslash ).$