A tapered circular bar is rigidly fixed at both the ends as shown in Fig. 13.45. If the temperature is raised by \(50^{\circ} \mathrm{C}\), calculate the stress in the bar. Take \(E=202 \mathrm{GPa}\) and \(\alpha=12 \times 10^{-6}\) per \({ }^{\circ} \mathrm{C}\).

\[ d_{l}=80 \mathrm{~mm}, d_{2}=120 \mathrm{~mm}, l=1.0 \mathrm{~m} \]

x dx d d Fig. 13.45 d