399_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 399_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 5.5-2 A steel wire ( E ± 200 GPa) of diameter d ± 1.25 mm is bent around a pulley of radius R 0 ± 500 mm (see figure). (a) What is the maximum stress s max in the wire? (b) By what percent does the stress increase or decrease if the radius of the pulley is increased by 25%? SECTION 5.5 Normal Stresses in Beams 393 Solution 5.5-2 (a) M AX . NORMAL STRESS IN WIRE s max ± 250 MPa ; s ± E d 2 r s max ± E d 2 R 0 + d 2 E ± 200 GPa d ± 1.25 mm R 0 ± 500 mm (b) % C HANGE IN MAX . STRESS DUE TO INCREASE IN PULLEY RADIUS BY 25% ; s new ² s max s max (100) ±² 20% s new ± 199.8 MPa s new ± E d 2 1.25 R 0 + d 2 d R 0 Problem 5.5-3 A thin, high-strength steel rule ( E ± 30 ³ 10 6 psi) having thickness t ± 0.175 in. and length L ± 48 in. is bent by couples M 0 into a circular are subtending a central angle a ±
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Unformatted text preview: 40° (see figure). (a) What is the maximum bending stress s max in the rule? (b) By what percent does the stress increase or decrease if the central angle is increased by 10%? L = length M M t a Solution 5.5-3 (a) M AX . BENDING STRESS ; s max ± 38.2 ksi s max ± Et a 2 L s max ± E t 2 r s max ± Et 2 r r ± L a r ± 68.755 inches E ± 30 (10 6 ) psi L ± 48 inches t ± 0.175 in. a ± 40 a p 180 b a ± 0.698 radians (b) % C HANGE IN STRESS DUE TO 10% INCREASE IN ANGLE linear increase (%) ; s new ² s max s max (100) ± 10% s new ± E t (1.1 a ) 2 L s new ± 41997 psi a 05Ch05.qxd 9/24/08 4:59 AM Page 393...
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