Solved: A rod consisting of two cylindrical portions AB and BC is restrained at both

Chapter 9, Problem 9.42

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A rod consisting of two cylindrical portions AB and BC is restrained at both ends. Portion AB is made of steel \(\left(E_{s}=29 \times 10^{6} \mathrm{\ psi}, \ \alpha_{s}=\right.\left.6.5 \times 10^{-6} /{ }^{\circ} \mathrm{F}\right)\) and portion BC is made of brass \(\left(E_{b}=15 \times 10^{6} \mathrm{\ psi}, \ \alpha_{b}=\right.\left.10.4 \times 10^{-6} /{ }^{\circ} \mathrm{F}\right)\). Knowing that the rod is initially unstressed, determine (a) the normal stresses induced in portions AB and BC by a temperature rise of \(65^{\circ} \mathrm{F}\), (b) the corresponding deflection of point B.