A switching device consist of a rectangular cross$-$section metal cantilever $200$ mm in length

and $30$ mm in width. The required operating displacement at the free end is $2\mathrm{.}7$ mm and

the service life is to be $100000$ cycles. To allow for the scatter of life performance a factor

of $5$ is employed on endurance.

Using the fatigue curves presented in Figure $2$ below, determine the required thickness of

the cantilever if made in $($a$)$ Mild steel, $($b$)$ aluminium alloy. ESteel $=208$ GPa,

Ealuminium $=79$ GPa.