Find the temperature stresses when the expansion of the rod is fully prevented.

$\text { Take, } \alpha=12 \times 10^{-6} \text { per }^{0} \mathrm{C} . \quad \mathrm{E}=2 \times 10^{5} \mathrm{N} / \mathrm{mm}^{2}$ $$ \begin{array}{l}{\text { Data: } L=15 m \quad t_{1}=15^{\circ} C t_{2}=65^{\circ} \mathrm{C} \quad \alpha=12 \times 10^{-6} /^{\circ} \mathrm{C}} \ {E=2 \times 10^{5} \mathrm{N} / \mathrm{mm}^{2}} \ {\text { Find: } \delta L_{t}=? \sigma_{t}=?} \ {\mathrm{t}=t_{1}-t_{2}=50^{\circ} \mathrm{C}}\end{array} $$

$$ \begin{array}{l}{\delta L_{t}=\alpha \times t \times L} \\ {\delta L_{t}=12 \times 10^{-6} \times 50 \times 15 \times 10^{3}} \\ {\delta L_{t}=9 m m} \\ {\sigma_{t}=\alpha \times t \times E} \\ {\sigma_{t}=12 \times 10^{-6} \times(65-15) \times 2 \times 10^{5}} \\ {\sigma_{t}=120 N / m m^{2}}\end{array} $$