$3.$ Based on Model Problem $10\mathrm{.}4$ discussed in class, for a circular rod made of $2014-$T$6$ alloy $($see digital page $742$ of the textbook$),$ as shown in Figure $3,$ determine:

a$)$ The smallest diameter of the rod that can safely support a centric load of $\backslash (\backslash$mathrm$\{$P$\}=80\backslash$mathrm$\{$kN$\}\backslash )$ for:

I. $\backslash ($ L$=800\backslash$mathrm$\{$~mm$\}\backslash ),$

II$.\backslash ($ L$=500\backslash$mathrm$\{$~mm$\}\backslash )$

Figure $3.$ Adaptation of Model Problem $10\mathrm{.}4.$