03-03ChapGere.0010

03-03ChapGere.0010 - 2 p (5.5 in.) 2 (1.0 in.) 5 6314 psi...

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Thin-Walled Tubes Problem 3.10-1 A hollow circular tube having an inside diameter of 10.0 in. and a wall thickness of 1.0 in. (see figure) is subjected to a torque T 5 1200 k-in. Determine the maximum shear stress in the tube using (a) the approximate theory of thin-walled tubes, and (b) the exact torsion theory. Does the approximate theory give conservative or nonconservative results? Solution 3.10-1 Hollow circular tube SECTION 3.10 Thin-Walled Tubes 245 10.0 in. 1.0 in. 10.0 in. 1.0 in. T 5 1200 k-in. t 5 1.0 in. r 5 radius to median line r 5 5.5 in. d 2 5 outside diameter 5 12.0 in. d 1 5 inside diameter 5 10.0 in. A PPROXIMATE THEORY (E Q . 3-63) E XACT THEORY (E Q . 3-11) Because the approximate theory gives stresses that are too low, it is nonconservative. Therefore, the approximate theory should only be used for very thin tubes. t exact 5 6830 psi 5 6831 psi 5 16(1200 k-in.)(12.0 in.) p [(12.0 in.) 4 2 (10.0 in.) 4 ] t 2 5 T ( d 2 / 2) I P 5 Td 2 2 ¢ p 32 d 2 4 2 d 1 4 t approx 5 6310 psi t 1 5 T 2 p r 2 t 5 1200 k-in.
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Unformatted text preview: 2 p (5.5 in.) 2 (1.0 in.) 5 6314 psi Problem 3.10-2 A solid circular bar having diameter d is to be replaced by a rectangular tube having cross-sectional dimensions d 3 2 d to the median line of the cross section (see figure). Determine the required thickness t min of the tube so that the maxi-mum shear stress in the tube will not exceed the maximum shear stress in the solid bar. Solution 3.10-2 Bar and tube t 2 d t d d S OLID BAR (Eq. 3-12) R ECTANGULAR TUBE t max 5 16 T p d 3 A m 5 ( d )(2 d ) 5 2 d 2 (Eq. 3-64) (Eq. 3-61) E QUATE THE MAXIMUM SHEAR STRESSES AND SOLVE FOR t If t . t min , the shear stress in the tube is less than the shear stress in the bar. t min 5 p d 64 16 T p d 3 5 T 4 td 2 t max 5 T 2 tA m 5 T 4 td 2 d t 2 d d A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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