Three rods of different materials are connected and placed between rigid supports at A and $D,$ as shown. Properties for each of the three rods are given in the accompanying table. The bars are initially unstressed when the structure is assembled at $20C.$ After the temperature has been increased to $70C,$ determine

$($a$)$ the normal stresses in the three rods.

$($b$)$ the force exerted on the rigid supports.

$($c$)$ the deflections of joints $B$ and $C$ relative to rigid support $A.$

$\backslash$table$[[$Aluminum $(1),$Cast Iron $(2),$Bronze $(3)],[L_1=440mm,L_2=150mm,L_3=320mm$