440_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

440_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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434 CHAPTER 5 Stresses in Beams (Basic Topics) evaluate using numerical data s max ± 25.2 MPa ; s max ± (2400) (8) 3 p (0.010) (0.090) 2 d B ± 270 mm t ± 10 mm d A ± 90 mm P ± 2.4 kN L ± 8 m s max ± PL 3 p t d A 2 s max ± J ² 4 P L 4 a ² L ³ L 4 b L p t d A 2 a L ³ 2 L 4 b 2 K s max ± s a L 4 b stress at support M AX . MOMENT AT L/2 SO COMPARE Stress at location of max. moment s max / s ( L /2) ± PL 3 p td A 2 a 1 4 P L p td A 2 b ± 4 3 ; s a L 2 b ± 1 4 P L p td A 2 s a L 2 b ±² 4 P L 2 a ² L ³ L 2 b L p td A 2 a L ³ 2 L 2 b 2 s B ± 0 so no ratio of s max / s B is possible s B ±² 4 PL ( ² L + L ) L p td A 2 ( L + 2 L 2 ) s B ± s ( L ) Problem 5.7-3 A tapered cantilever beam AB having rectangular cross sections is subjected to a concentrated load P ± 50 lb and a couple M 0 ± 800 lb-in. acting at the free end [see figure part (a)]. The width b of the beam is constant and equal to 1.0 in., but the height varies linearly from h A ± 2.0 in. at the loaded end to h B ± 3.0 in. at the support. (a) At what distance x from the free end does the maximum bending stress
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Unformatted text preview: s max occur? What is the magnitude s max of the maximum bending stress? What is the ratio of the maximum stress to the largest stress s B at the support? (b) Repeat (a) if, in addition to P and M , a triangular distributed load with peak intensity q ± 3 P / L acts upward over the entire beam as shown. What is the ratio of the maximum stress to the stress at the location of maximum moment? (a) h A = 2.0 in. h B = 3.0 in. B A b = 1.0 in. b = 1.0 in. x P = 50 lb M = 800 lb-in. L = 20 in. (b) B A x P = 50 lb M = 800 lb-in. L = 20 in. 3 P L — q = 05Ch05.qxd 9/24/08 4:59 AM Page 434...
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