03-03ChapGere.0014

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Solution 3.10-8 Regular hexagon SECTION 3.10 Thin-Walled Tubes 249 t b b 5 Length of side t 5 Thickness L m 5 6 b F ROM A PPENDIX D, C ASE 25: b 5 60 8 n 5 6 5 3 Ï 3 b 2 2 A m 5 nb 2 4 cot b 2 5 6 b 2 4 cot 30 8 S HEAR STRESS A NGLE OF TWIST PER UNIT LENGTH ( RATE OF TWIST ) (radians per unit length) u 5 T GJ 5 2 T G (9 b 3 t ) 5 2 T 9 Gb 3 t J 5 4 A m 2 t # L m 0 d S t 5 4 A m 2 t L m 5 9 b 3 t 2 t 5 T 2 tA m 5 T Ï 3 9 b 2 t Problem 3.10-9 Compare the angle of twist f 1 for a thin-walled circular tube (see figure) calculated from the approximate theory for thin-walled bars with the angle of twist f 2 calculated from the exact theory of torsion for circular bars. (a) Express the ratio f 1 / f 2 in terms of the nondimensional ratio b 5 r / t . (b) Calculate the ratio of angles of twist for b 5 5, 10, and 20. What conclusion about the accuracy of the approximate theory do you draw from these results?
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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 Tech.

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