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410_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 410_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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404 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.5-17 N UMERICAL DATA M Amax (12) ± 23640 in.-lb M Amax ± 1970 ft-lb M Amax ± 22.5 (8) 2 2 + 250 (5) ft-lb c 2 ± 2.269 in. I ± 3.36 in. 4 c 1 ± 0.617 in. M AXIMUM STRESSES ; s c ± M Amax c 2 I s c ± 15964 psi ; s t ± M Amax c 1 I s t ± 4341 psi Problem 5.5-18 A cantilever beam AB of isosceles trapezoidal cross section has length L ± 0.8 m, dimensions b 1 ± 80 mm, b 2 ± 90 mm, and height h ± 110 mm (see figure). The beam is made of brass weighing 85 kN/m 3 . (a) Determine the maximum tensile stress s t and maximum compressive stress s c due to the beam’s own weight. (b) If the width b 1 is doubled, what happens to the stresses? (c) If the height h is doubled, what happens to the stresses? b 2 b 1 q L h C Solution 5.5-18 N UMERICAL DATA (a) M AX . STRESSES DUE TO BEAM S OWN WEIGHT I ± 9.417 * 10 6 mm 4 I ± h 3 1 b 1 2 ² 4 b 1 b 2 ² b 2 2 2 36 ( b 1 ² b 2 ) y bar ± h (2
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Unformatted text preview: b 1 ² b 2 ) 3 ( b 1 ² b 2 ) y bar ± 53.922 mm M max ± 254.32 N # m q ± 7.9475 * 10 2 N m A ± 9.35 * 10 3 mm 2 M max ± q L 2 2 q ± g A A ± 1 2 ( b 1 + b 2 ) h h ± 110 mm b 1 ± 80 mm b 2 ± 90 mm L ± 0.8 m g ± 85 kN m 3 M AX . TENSILE STRESS AT SUPPORT ( TOP ) M AX . COMPRESSIVE STRESS AT SUPPORT ( BOTTOM ) (b) D OUBLE b 1 & RECOMPUTE STRESSES y bar ± h (2 b 1 + b 2 ) 3 ( b 1 + b 2 ) y bar ± 60.133 mm M max ± 374 N # m M max ± qL 2 2 q ± g A q ± 1.169 * 10 3 N m A ± 1 2 ( b 1 + b 2 ) h A ± 1.375 * 10 4 mm 2 b 1 ± 160 mm ; s c ± M max y bar I s c ± 1.456 MPa ; s t ± M max ( h ³ y bar ) I s t ± 1.514 MPa 05Ch05.qxd 9/24/08 4:59 AM Page 404...
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