A steel rail exactly 20 m long at $-10^{0} \mathrm{C}$ is firmly clampled between two fixed supports

Question

A steel rail exactly 20 m long at $-10^{0} \mathrm{C}$ is firmly clampled between two fixed supports exactly 20 m apart. The force of compression in the rails will be, if the temperature rises to $30^{0} \mathrm{C}$ (the rail's cross sectional area is $50 \mathrm{~cm}^{2}$ also). Take $\mathrm{Y}=20 	imes 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ and coefficient of linear expansion $1.1 	imes 10^{-5} /{ }^{0} \mathrm{C}$\

Professor PC Thomas Classes · Answer

$\mathrm{F}=\mathrm{YA} \alpha \Delta 	heta$\ $\mathrm{Y}=20 	imes 10^{10} \mathrm{~N} / \mathrm{m}^{2}$\ $\mathrm{A}=50 \mathrm{~cm}^{2}=\mathrm{m}^{2}$\ $\alpha=\alpha_{1}=1.1 	imes 10^{-5} /{ }^{0} \mathrm{C}$\ $\Delta 	heta=30-(-10)=40^{\circ} \mathrm{C}$\ Substitute and get F.