The assembly has the diameters and material indicated.

a$)$ If it fits securely between its fixed supports when the temperature is $\backslash ($ T$\_\{1\}=70^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ),$ determine the average normal stress in each material when the temperature reaches $\backslash ($ T$\_\{2\}=110^\{\backslash$circ$\}\backslash$mathrm$\{$F$\}\backslash ).$

b$)$ Calculate the factor of safety for each of these segments and note if any of them fail when the temperature is increased as described in part a$.$

Please use the "force method of analysis" to solve this problem $($Hibbeler V$11,$ chapter $4\mathrm{.}4).$