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05-06ChapGere.0011 - that should be used in the notches(b...

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Problem 5.13-4 A rectangular beam with semicircular notches, as shown in part (b) of the figure, has dimensions h 120 mm and h 1 100 mm. The maximum allowable bending stress in the plastic beam is max 6 MPa, and the bending moment is M 150 N m. Determine the minimum permissible width b min of the beam. Solution 5.13-4 Beam with semicircular notches SECTION 5.13 Stress Concentrations 373 h 120 mm h 1 100 mm max 6 MPa M 150 N m h h 1 2 R From Fig. 5-50: K 2.20 R h 1 10 mm 100 mm 0.10 R 1 2 ( h h 1 ) 10 mm Solve for b : b min 33 mm 6 MPa (2.20) B 6(150 N m) b (100 mm) 2 R s max K s nom K ¢ 6 M bh 2 1 Problem 5.13-5 A rectangular beam with notches and a hole (see figure) has dimensions h 5.5 in., h 1 5 in., and width b 1.6 in. The beam is subjected to a bending moment M 130 k-in., and the maximum allowable bending stress in the material (steel) is max 42,000 psi. (a) What is the smallest radius
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Unformatted text preview: that should be used in the notches? (b) What is the diameter d max of the largest hole that should be drilled at the midheight of the beam? Solution 5.13-5 Beam with notches and a hole M M d h 1 h 2 R h 5 5.5 in. h 1 5 5 in. b 5 1.6 in. M 5 130 k-in. s max 5 42,000 psi (a) M INIMUM NOTCH RADIUS From Fig. 5-50, with K 5 2.15 and , we get [ R min ø 0.090 h 1 5 0.45 in. R h 1 < 0.090 h h 1 5 1.1 K 5 s max s nom 5 42,000 psi 19,500 psi 5 2.15 s nom 5 6 M bh 2 1 5 19,500 psi h h 1 5 5.5 in. 5 in. 5 1.1 (b) L ARGEST HOLE DIAMETER Assume and use Eq. (5-56). or d 3 1 23.21 d 2 166.4 5 Solve numerically: d max 5 4.13 in. 42,000 psi 5 12(130 k-in.) d (1.6 in.) [ (5.5 in.) 3 2 d 3 ] s B 5 12 Md b ( h 3 2 d 3 ) d h 7 1 2 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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