03-03ChapGere.0013

# 03-03ChapGere.0013 - t 5 T 2 tA m 5 18 k-in 2(0.2 in(18.850...

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Problem 3.10-7 A thin-walled steel tube having an elliptical cross section with constant thickness t (see figure) is subjected to a torque T 5 18 k-in. Determine the shear stress t and the rate of twist u (in degrees per inch) if G 5 12 3 10 6 psi, t 5 0.2 in., a 5 3 in., and b 5 2 in. ( Note: See Appendix D, Case 16, for the properties of an ellipse.) Solution 3.10-7 Elliptical tube 248 CHAPTER 3 Torsion t 2 a 2 b T 5 18 k-in. G 5 12 3 10 6 psi t 5 constant t 5 0.2 in a 5 3.0 in. b 5 2.0 in. F ROM APPENDIX D, CASE 16: A m 5 p ab 5 p (3.0 in.)(2.0 in.) 5 18.850 in. 2 S HEAR STRESS A NGLE OF TWIST PER UNIT LENGTH ( RATE OF TWIST ) u 5 83.73 3 10 2 6 rad / in. 5 0.0048 8 / in. u 5 f L 5 T GJ 5 18 k-in. (12 3 10 6 psi)(17.92 in. 4 ) 5 2390 psi
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Unformatted text preview: t 5 T 2 tA m 5 18 k-in. 2(0.2 in.)(18.850 in. 2 ) 5 17.92 in. 4 J 5 4 tA m 2 L m 5 4(0.2 in.)(18.850 in. 2 ) 2 15.867 in. 5 p [1.5(5.0 in.) 2 Ï 6.0 in. 2 ] 5 15.867 in. L m < p [1.5( a 1 b ) 2 Ï ab ] t 2 a 2 b Problem 3.10-8 A torque T is applied to a thin-walled tube having a cross section in the shape of a regular hexagon with constant wall thickness t and side length b (see figure). Obtain formulas for the shear stress t and the rate of twist u . t b A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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