(Solution) - A circular steel rod AB diameter d1 1 0 in -(2025 Original AI-Free Solution)

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A circular steel rod AB (diameter d1 = 1.0 in., length L1 = 3.0 ft) has a bronze sleeve (outer diameter d2 = 1.25 in., length L2 = 1.0 ft) shrunk onto it so that the two parts are securely bonded (see figure).
Calculate the total elongation ? of the steel bar due to a temperature rise ?T = 500°F. (Material properties are as follows: for steel, Es = 30 × 106 psi and ?s = 6.5 × 106 / °F; for bronze, Eb = 15 × 106 psi and ?b = 11 × 106 / °F.)