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Problem 3.10-13 A long, thin-walled tapered tube AB of circular cross section (see figure) is subjected to a torque T . The tube has length L and constant wall thickness t . The diameter to the median lines of the cross sections at the ends A and B are d A and d B , respectively. Derive the following formula for the angle of twist of the tube: f 5 } p 2 T G L t } 1 } d A 1 d 2 A d 2 B } d B 2 Hint: If the angle of taper is small, we may obtain approximate results by applying the formulas for a thin-walled prismatic tube to a differential element of the tapered tube and then integrating along the axis of the tube. Solution 3.10-13 Thin-walled tapered tube SECTION 3.10 Thin-Walled Tubes 253 t t L TT A B d A d B L x dx A B d(x) d A d B t 5 thickness d A 5 average diameter at end A d B 5 average diameter at end B T 5 torque d ( x ) 5 average diameter at distance
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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