Problem $4(4-85)$

The center rod $CD$ of the assembly is heated from $T_1=30$ to $T_2=180C$ using electrical resistance heating. Also, the two end rods $AB$ and $EF$ are heated $T_1=30$ to $T_2=50C.$ At the lower temperature $T1$ the gap between $C$ and the rigid bar 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 $125m{m}^2.CD$ is made of aluminum and has a cross$-$sectional area of $375m{m}^2.E_{ST}=200[GPa],E_{AL}=70[GPa],{}_{ST}=12*{10}^{-6}\frac{1}{}C,$ and ${}_{AL}=23*{10}^{-6}[\frac{1}{}C]$

Ans: $F_{AB}=F_{EF}=1\mathrm{.}85kN,F_{CD}=3\mathrm{.}70kN$