05-01ChapGere.0005

05-01ChapGere.0005 - (a) What is the maximum bending stress...

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Problem 5.5-2 A steel wire ( E 5 200 GPa) of diameter d 5 1.0 mm is bent around a pulley of radius R 0 5 400 mm (see figure). (a) What is the maximum stress s max in the wire? (b) Does the stress increase or decrease if the radius of the pulley is increased? Solution 5.5-2 Steel wire bent around a pulley SECTION 5.5 Normal Stresses in Beams 289 d R 0 E 5 200 GPa d 5 1.0 mm R 0 5 400 mm (a) M AXIMUM STRESS IN THE WIRE y 5 d 2 5 0.5 mm r 5 R 0 1 d 2 5 400 mm 1 0.5 mm 5 400.5 mm From Eq. (5-7): (b) C HANGE IN STRESS If the radius is increased, the stress s max decreases. s max 5 Ey r 5 (200 GPa) (0.5 mm) 400.5 mm 5 250 MPa Problem 5.5-3 A thin, high-strength steel rule ( E 5 30 3 10 6 psi) having thickness t 5 0.15 in. and length L 5 40 in. is bent by couples M 0 into a circular arc subtending a central angle a 5 45° (see figure).
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Unformatted text preview: (a) What is the maximum bending stress s max in the rule? (b) Does the stress increase or decrease if the central angle is increased? Solution 5.5-3 Thin steel rule bent into an arc L = length M M t a E 5 30 3 10 6 psi t 5 0.15 in. L 5 40 in. a 5 45 5 0.78540 rad (a) M AXIMUM BENDING STRESS s max 5 Ey r 5 E ( t / 2) L / a 5 Et a 2 L L 5 r a r 5 L a a 5 radians Substitute numerical values: 5 44,200 psi 5 44.2 ksi (b) C HANGE IN STRESS If the angle a is increased, the stress s max increases. s max 5 (30 3 10 6 psi) (0.15 in.) (0.78540 rad) 2 (40 in.) L a r A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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