A circular steel rod AB (diameter d1=15 mm, length L1=1100 mm) has a bronze sleeve (outer diameter d2 21 mm, length L2=800 mm) shrunk onto it so that the two parts are securely bonded (see figure). Calculate the total elongation δ (mm) of the steel bar due to a temperature rise ΔT=200oC. (Material properties are as follows: for steel, Es=210 GPa and αs=12x10-6/C; for bronze, Eb=110 GPa and αb=20x10-6/C.

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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A circular steel rod AB (diameter d1=15 mm, length L1=1100 mm) has a bronze sleeve (outer diameter d2 21 mm, length L2=800 mm) shrunk onto it so that the two parts are securely bonded (see figure). Calculate the total elongation δ (mm) of the steel bar due to a temperature rise ΔT=200oC. (Material properties are as follows: for steel, Es=210 GPa and αs=12x10-6/C; for bronze, Eb=110 GPa and αb=20x10-6/C.)
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Would it be possible to get a solution for this without using the composite beam equation? Or to at least derive the composite beam equation?

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