256_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

256_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.2.qxd 9/27/08 250 1:05 PM Page 250 CHAPTER 3 Torsion Solution 3.2-2 NUMERICAL DATA d 56 mm a 0.012 radians 4a f p b radians 180 solution based on Equ. (3-3): 162.9 mm Lmin Lmin df 2a ; Problem 3.2-3 A circular aluminum tube subjected to pure torsion by torques T (see figure) has an outer radius r2 equal to 1.5 times the inner radius r1. T T L (a) If the maximum shear strain in the tube is measured as 400 10 6 rad, what is the shear strain 1 at the inner surface? (b) If the maximum allowable rate of twist is 0.125 degrees per foot and the maximum shear strain is to be kept at 400 10 6 rad by adjusting the torque T, what is the minimum required outer radius (r2)min? r2 r1 Probs. 3.2-3, 3.2-4, and 3.2-5 Solution 3.2-3 NUMERICAL DATA r2 1.5r1 u 0.125 a (b) MIN. REQUIRED OUTER RADIUS 400 max (10 6) radians r2min p 1 ba b 180 12 1.818 10 4 r2min max u r2min 2.2 inches max u ; rad /m. (a) SHEAR STRAIN AT INNER SURFACE AT RADIUS r1 1 r1 r2 1 267 max 10 1 6 1 1.5 radians max ; Problem 3.2-4 A circular steel tube of length L 1.0 m is loaded in torsion by torques T (see figure). (a) If the inner radius of the tube is r1 45 mm and the measured angle of twist between the ends is 0.5°, what is the shear strain 1 (in radians) at the inner surface? (b) If the maximum allowable shear strain is 0.0004 rad and the angle of twist is to be kept at 0.45° by adjusting the torque T, what is the maximum permissible outer radius (r2)max? ...
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