Question: Compare the angle of twist (1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of

Compare the angle of twist (1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist (2 calculated from the exact theory of torsion for circular bars.
(a) Express the ratio (1/(2 in terms of the nondimensional ratio ( = r/t.
(b) Calculate the ratio of angles of twist for ( = 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?

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