$2.($a$).($i$).$Define a compound bar

$($ii$).$Using labeled sketches derive the compatibility and equilibrium equation. $(8$ Marks$)$

$($b$).$A short rigid horizontal bar is suspended from a rigid support by a central vertical steel bar $8$ mm diameter $3\mathrm{.}6$ m long, and two symmetrically placed copper bars $16$ mm diameter $3$ m long.The rigid bar is loaded with a centrally placed load of $40$ KN $.$

Determine the loads carried in each bar and the extension in each bar.

Take Esteel $\backslash (=205\backslash$mathrm$\{$KN$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash$quad $\backslash )$ Ecopper $\backslash (=93\backslash$mathrm$\{$KN$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash )$

$(12$ Marks$)$