Q$2$: $(12$ points$)$ The cylinder CD of the assembly is heated from $\backslash (\backslash$mathrm$\{$T$\}1=30\backslash )$ degree Celsius to T$2\backslash (=180\backslash )$ degree Celsius using electrical resistance. At the lower temperature T$1$ the gap between C and the rigid bar, BF is $0\mathrm{.}7$ mm $.$ Determine the force in rods AB and EF caused by the increase in temperature. Rods AB and EF are made of steel and each has a cross sectional area of $125\backslash (\backslash$mathrm$\{$mm$\}^\{2\}.\backslash$mathrm$\{$CD$\}\backslash )$ is made of aluminum and has a cross section area of $\backslash (375\backslash$mathrm$\{$~mm$\}^\{2\}\backslash ).$ Modulus of elasticity of steel and aluminum are $200$ GPa and $70$ GPa $,$ coefficient of thermal expansion is $\backslash (23\backslash$mathrm$\{$X$\}10\backslash$mathrm$\{$E$\}-6\backslash )/$degree Celsius.