05-06ChapGere.0010

# 05-06ChapGere.0010 - 372 A-PDF Stresses in Beams CHAPTER 5...

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Problem 5.13-2 The beams shown in the figure are subjected to bending moments M 5 250 N ? m. Each beam has a rectangular cross section with height h 5 44 mm and width b 5 10 mm (perpendicular to the plane of the figure). (a) For the beam with a hole at midheight, determine the maximum stresses for hole diameters d 5 10, 16, 22, and 28 mm. (b) For the beam with two identical notches (inside height h 1 5 40 mm), determine the maximum stresses for notch radii R 5 2, 4, 6, and 8 mm. Solution 5.13-2 372 CHAPTER 5 Stresses in Beams M 5 250 N ? m h 5 44 mm b 5 10 mm (a) B EAM WITH A HOLE Eq. (5-57): (1) Eq. (5-56): (2) Note: The larger the hole, the larger the stress. s C s B dd Eq.(1) Eq.(2) s max (mm) h (MPa) (MPa) (MPa) 10 0.227 78 78 16 0.364 81 81 22 0.500 89 89 89 28 0.636 133 133 5 300 3 10 3 d 85,180 2 d 3 MPa s B 5 12 Md b ( h 3 2 d 3 ) d h \$ 1 2 5 6.6 3 10 6 85,180 2 d 3 MPa s C 5 6 Mh b ( h 3 2 d 3 ) d h # 1 2 (b) B EAM WITH NOTCHES h 1 5 40 mm Eq. (5-58): s max 5 K s nom Note: The larger the notch radius, the smaller the stress. RR K s max (mm) h 1 (Fig. 5-50) (MPa) 2 0.05
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