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Narrow bars of aluminum are bonded to the two sides of a
Chapter 2, Problem 2.121(choose chapter or problem)
Narrow bars of aluminum are bonded to the two sides of a thick steel plate as shown. Initially, at \(T_{1}=70^{\circ} \mathrm{F}\), all stresses are zero. Knowing that the temperature will be slowly raised to \(T_{2}\) and then reduced to \(T_{1}\), determine (a) the highest temperature \(T_{2}\) that does not result in residual stresses, (b) the temperature \(T_{2}\) that will result in a residual stress in the aluminum equal to 58 ksi. Assume \(\alpha_{a}=12.8 \times 10^{-6} /{ }^{\circ} \mathrm{F}\) for the aluminum and \(\alpha_{s}=6.5 \times 10^{-6} /{ }^{\circ} \mathrm{F}\) for the steel. Further assume that the aluminum is elastoplastic with \(E=10.9 \times 10^{6}\) psi and \(\alpha_{Y}=58 \mathrm{ksi}\). (Hint: Neglect the small stresses in the plate.)
Questions & Answers
QUESTION:
Narrow bars of aluminum are bonded to the two sides of a thick steel plate as shown. Initially, at \(T_{1}=70^{\circ} \mathrm{F}\), all stresses are zero. Knowing that the temperature will be slowly raised to \(T_{2}\) and then reduced to \(T_{1}\), determine (a) the highest temperature \(T_{2}\) that does not result in residual stresses, (b) the temperature \(T_{2}\) that will result in a residual stress in the aluminum equal to 58 ksi. Assume \(\alpha_{a}=12.8 \times 10^{-6} /{ }^{\circ} \mathrm{F}\) for the aluminum and \(\alpha_{s}=6.5 \times 10^{-6} /{ }^{\circ} \mathrm{F}\) for the steel. Further assume that the aluminum is elastoplastic with \(E=10.9 \times 10^{6}\) psi and \(\alpha_{Y}=58 \mathrm{ksi}\). (Hint: Neglect the small stresses in the plate.)
ANSWER:
Step 1 of 3
We will find the temperature just required to cause yielding. That will be the highest possible temperature. We will then calculate residual stress based on given stress and then the corresponding temperature will be calculated.