Rigid bar ABCD is supported by two bars. There is no strain in the vertical bars before load $P$ is applied. After load $P$ is applied, the normal strain in bar $(2)$ is measured as $-4200\frac{m}{m}.$ Use the dimensions $L_1=1800mm,L_2=1350\mathrm{.}00mm,a=220mm,b=440mm,$ and $c=165mm.$ Determine:

$($a$)$ the normal strain in bar $(1).$

$($b$)$ the normal strain in bar $(1)$ if there is a $=1mm$ gap in the connection at pin $C$ before the load is applied.

$($c$)$ the normal strain in bar $(1)$ if there is a $=1mm$ gap in the connection at pin $B$ before the load is applied.