499_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

499_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 5.13 Stress Concentrations 493 R (mm) R h 1 K (Fig. 5-50) (MPa) s max s max ± K s nom 2 0.05 2.6 240 4 0.10 2.1 200 6 0.15 1.8 170 8 0.20 1.7 160 d (mm) d h Eq. (1) (MPa) s c Eq. (2) (MPa) s B (MPa) s max 10 0.227 78 78 16 0.364 81 81 22 0.500 89 89 89 28 0.636 133 133 Problem 5.13-2 The beams shown in the figure are subjected to bending moments . Each beam has a rectangular cross section with height and width (perpendicular to the plane of the figure). (a) For the beam with a hole at midheight, determine the maximum stresses for hole diameters and . (b) For the beam with two identical notches (inside height ), determine the maximum stresses for notch radii , and . 8 mm R ± 2, 4, 6 h 1 ± 40 mm 28 mm d ± 10, 16, 22 b ± 10 mm h ± 44 mm M ± 250 N # m Solution 5.13-2 (a) B EAM WITH A HOLE s B ± 12 Md b ( h 3 ² d 3 ) ± 300 * 10 3 d 85,180 ² d 3 MPa (2) d h Ú 1 2 Eq. (5-56): s c ± 6 Mh b ( h 3 ² d 3 ) ± 6.6 * 10
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Unformatted text preview: 6 85,180 ² d 3 MPa (1) d h … 1 2 Eq. (5-57): M ± 250 N # m h ± 44 mm b ± 10 mm (b) B EAM WITH NOTCHES Eq. (5-58): s nom ± 6 M bh 1 2 ± 93.8 MPa h 1 ± 40 mm h h 1 ± 44 mm 40 mm ± 1.1 NOTE: The larger the hole, the larger the stress. NOTE: The larger the notch radius, the smaller the stress. Problem 5.13-3 A rectangular beam with semicircular notches, as shown in part (b) of the figure, has dimensions in. and in. The maximum allowable bending stress in the metal beam is , and the bending moment is . Determine the minimum permissible width of the beam. b min M ± 600 lb-in s max ± 60 ksi h 1 ± 0.80 h ± 0.88 05Ch05.qxd 9/25/08 2:29 PM Page 493...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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