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498_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

498_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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492 CHAPTER 5 Stresses in Beams (Basic Topics) Solution 5.13-1 (a) B EAM WITH A HOLE 67,200 d 3.375 d 3 (2) d h Ú 1 2 Eq.(5-56): s B 12 Md b ( h 3 d 3 ) 50,400 3.375 d 3 (1) d h 1 2 Eq.(5-57): s c 6 Mh b ( h 3 d 3 ) M 2100 lb-in. h 1.5 in. b 0.375 in. Thus, this composite section has no tensile stress s c P A + Pe I c ; y 0 148.3 mm 7 h 133.4 mm ; P max 149.6 kN P s c 1 A + e I c Stress Concentrations The problems for Section 5.13 are to be solved considering the stress-concentration factors. Problem 5.13-1 The beams shown in the figure are subjected to bending moments -in. 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 1.00 in. (b) For the beam with two identical notches (inside height .), determine the maximum stresses for notch radii
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Unformatted text preview: . 0.20 in R ± 0.05, 0.10, 0.15, h 1 ± 1.25 in d ± 0.25, 0.50, 0.75 b ± 0.375 in. h ± 1.5 in. M ± 2100 lb (b) (a) M M M M d h h h 1 2 R Probs. 5.13.1 through 5.13-4 R (in) R h 1 K (Fig. 5-50) (psi) s max s max ± K s nom 0.05 0.04 3.0 65,000 0.10 0.08 2.3 49,000 0.15 0.12 2.1 45,000 0.20 0.16 1.9 41,000 (b) B EAM WITH NOTCHES Eq. (5-58) s nom ± 6M bh 2 1 ± 21,500 psi h 1 ± 1.25 in. h h 1 ± 1.5 in. 1.25 in. ± 1.2 d (in.) d h Eq. (1) (psi) s c Eq. (2) (psi) s B (psi) s max 0.25 0.1667 15,000 — 15,000 0.50 0.3333 15,500 — 15,500 0.75 0.5000 17,100 17,100 17,100 1.00 0.6667 — 28,300 28,300 NOTE: The larger the hole, the larger the stress. NOTE: The larger the notch radius, the smaller the stress. 05Ch05.qxd 9/25/08 2:29 PM Page 492...
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