Solution Found!
An aluminum rod (Ea = 70 GPa, aa = 23.6 x 10- /C) and a
Chapter 2, Problem 2.57(choose chapter or problem)
An aluminum rod \(\left(E_{a}=70 \mathrm{GPa}, \alpha_{a}=23.6 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) and a steel link \(\left(E_{s}=200 \mathrm{GPa}, \alpha_{s}=11.7 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) have the dimensions shown at a temperature of \(20^{\circ} \mathrm{C}\). The steel link is heated until the aluminum rod can be fitted freely into the link. The temperature of the whole assembly is then raised to \(150^{\circ} \mathrm{C}\). Determine the final normal stress (a) in the rod, (b) in the link.
Questions & Answers
QUESTION:
An aluminum rod \(\left(E_{a}=70 \mathrm{GPa}, \alpha_{a}=23.6 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) and a steel link \(\left(E_{s}=200 \mathrm{GPa}, \alpha_{s}=11.7 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)\) have the dimensions shown at a temperature of \(20^{\circ} \mathrm{C}\). The steel link is heated until the aluminum rod can be fitted freely into the link. The temperature of the whole assembly is then raised to \(150^{\circ} \mathrm{C}\). Determine the final normal stress (a) in the rod, (b) in the link.
ANSWER:
Step 1 of 7
Change in temperature is
Unrestrained thermal expansion of each part:
Aluminum rod:
