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05-03ChapGere.0004

# 05-03ChapGere.0004 - 9(0.8 1 1.1(3 p(3 1 1 3 s A 5 s 1 x 5...

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Solution 5.7-4 Elliptical spokes in a flywheel 324 CHAPTER 5 Stresses in Beams (Basic Topics) P 5 15 kN 5 15,000 N M 0 5 12 kN ? m 5 12,000 N ? m L 5 1.1 m U NITS : Newtons, meters A T END A : b A 5 0.06 m, h A 5 0.09 m A T SUPPORT B : b B 5 0.08 m, h B 5 0.12 m A T DISTANCE x : Case 16, Appendix D: M x 5 M 0 1 Px 5 12,000 N ? m 1 (15,000 N) x 5 15,000(0.8 1 x ) 5 (80 3 10 9 )(0.8 1 x ) 3 p ¢ 3 1 x L 3 s 1 5 M x S x 5 15,000(0.8 1 x )(16 3 10 6 ) 9 p ¢ 3 1 x L 3 5 9 p 16 3 10 6 ¢ 3 1 x L 3 S x 5 p 32 (0.02) ¢ 3 1 x L (0.03) 2 ¢ 3 1 x L 2 I x 5 p 64 ( b x )( h x ) 3 Ê S x 5 I x h x / 2 5 p b x h x 2 32 I 5 p 64 ( bh 3 ) h x 5 h A 1 ( h B 2 h A ) x L 5 0.09 1 0.03 x L 5 0.03 ¢ 3 1 x L b x 5 b A 1 ( b B 2 b A ) x L 5 0.06 1 0.02 x L 5 0.02 ¢ 3 1 x L (a) A TEND A : x 5 0 5 251.5 MPa (b) A T END B : x 5 L 5 1.1 m 5 252.0 3 10 6 N/m 2 5 252.0 MPa (c) C ROSS SECTION OF MAXIMUM STRESS Set Evaluate the derivative, set it equal to zero, and solve for x . x 5 0.45 m (d) M AXIMUM BENDING STRESS 5 267.8 3 10 6 N/m 2 5 267.8 MPa s max 5 ( s 1 ) x 5 0.45 5 (80 3 10 9 )(0.8 1 0.45) (3 p ) ¢ 3 1 0.45 1.1 3 d s 1 dx 5 0 s B 5 ( s 1 ) x 5 L 5 (80 3 10
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Unformatted text preview: 9 )(0.8 1 1.1) (3 p )(3 1 1) 3 s A 5 ( s 1 ) x 5 5 (80 3 10 9 )(0.8) (3 p )(27) 5 251.5 3 10 6 N / m 2 x A P B M L = 1.10 m Problem 5.7-5 Refer to the tapered cantilever beam of solid circular cross section shown in Fig. 5-24 of Example 5-9. (a) Considering only the bending stresses due to the load P , determine the range of values of the ratio d B / d A for which the maximum normal stress occurs at the support. (b) What is the maximum stress for this range of values? A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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