The pin$-$connected structure shown in the figure consists of a rigid beam ABCD and two supporting bars. $B$ Bar $(1)$ is a bronze alloy $[E=93$GPa with a cross$-$sectional area of $A_1=220m{m}^2\frac{.}{B}ar(2)$ is an aluminum alloy $[[$:$E=69$GPa$\}$ with a cross$-$sectional area of $A_2=750m{m}^2.$ All bars are unstressed before the load $P$ is applied; however, there is a $4-mm$ clearance in the pin connection at $A.$ Assume $L_1=2000mm,a=870mm,b=510mm,c=410mm,$ and $L_2=1410mm.$ If a load of $P=136kN$ is applied at $B,$ determine

$($a$)$ the normal stresses in both bars $(1)$ and $(2).$

$($b$)$ the downward deflection of point $A$ on the rigid bar.