Two rods are joined together one behind the other and the extreme ends are built in the fixed supports. One rod is of steel \(3 \mathrm{~m}\) long and \(600 \mathrm{~mm}^{2}\) cross-sectional area. The other rod is of bronze \(0.8 \mathrm{~m}\) long and \(1200 \mathrm{~mm}^{2}\) cross-sectional area. There is no stress initially in the rods. Calculate the stresses set up in the rods if the temperature is dropped by \(50^{\circ} \mathrm{C}\).

\[E_{s}=200 \mathrm{GPa}, E_{b}=70 \mathrm{GPa}, \alpha_{a}=12 \times 10^{-6} \mathrm{per}^{\circ} \mathrm{C}, \alpha_{b}=18 \times 10^{-6} \mathrm{per}^{\circ} \mathrm{C}\]