Question: A thin-walled circular tube and a solid circular bar of the same material (see figure) are subjected to torsion. The tube and bar have the

A thin-walled circular tube and a solid circular bar of the same material (see figure) are subjected to torsion. The tube and bar have the same cross-sectional area and the same length.
What is the ratio of the strain energy U1 in the tube to the strain energy U2 in the solid bar if the maximum shear stresses are the same in both cases? (For the tube, use the approximate theory for thin-walled bars.)

Tube (1) Bar (2)

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