443_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

443_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 5.7-4 The spokes in a large flywheel are modeled as beams fixed at one end and loaded by a force P and a couple M 0 at the other (see figure). The cross sections of the spokes are elliptical with major and minor axes (height and width, respectively) having the lengths shown in the figure part (a). The cross-sectional dimensions vary linearly from end A to end B . Considering only the effects of bending due to the loads P and M 0 , determine the following quantities. (a) The largest bending stress s A at end A (b) The largest bending stress s B at end B (c) The distance x to the cross section of maximum bending stress (d) The magnitude s max of the maximum bending stress (e) Repeat (d) if uniform load q ( x ) ± 10 P /3 L is added to loadings P and M 0 , as shown in the figure part (b).
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Unformatted text preview: SECTION 5.7 Nonprismatic Beams 437 Solution 5.7-4 (a-d) F IND MAX . BENDING STRESS FOR TAPERED CANTILEVER numerical data S ( x ) p b A h A 2 a 1 + x 3 L b 3 32 S ( x ) p b ( x ) h ( x ) 2 32 I ( x ) p b ( x ) h ( x ) 3 64 S ( x ) I ( x ) h ( x ) 2 h ( x ) h A a 1 x 3 L b b ( x ) b A a 1 + x 3 L b P 12 kn M 10 kN # m b B 80 mm h B 120 mm L 1.25 m b A 60 mm h A 90 mm (b) (a) x A P = 12 kN B M = 10 kNm h B = 120 mm h A = 90 mm b B = 80 mm b A = 60 mm L = 1.25 m x A P B M L = 1.25 m 10 P 3 L q ( x ) = 0.5 1 10 20 30 M(x) (kNm) x (m) 0.5 1 200 210 220 230 240 (x) (MPa) x (m) 05Ch05.qxd 9/24/08 4:59 AM Page 437...
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