457_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

457_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/25/08 2:29 PM Page 451 451 SECTION 5.8 Shear Stresses in Rectangular Beams Solution 5.8-11 Wood platform with a plank deck Load on one plank: c q w(lb/ft2) 2 144 in. / ft 2 d (b in.) qa Reaction R wb (lb/in.) 144 96 in. b 2 (R a lb; w wb b (48) 144 lb/ft2; b wb 3 in.) Mmax occurs at midspan. Mmax Ra 3.5 in. 89 in. + b 2 2 wb (46.25) 3 Platform: 8 ft * 8 ft t (M thickness of planks wb (1152) 144 lb-in.; w 89 wb 12 lb/ft2; b in.) Allowable bending moment: 1.5 in. Mallow 2 uniform load on the deck (lb/ft ) w q(48 in.)2 3 s allow S (2400 psi)(0.375 b) 900 b (lb-in.) sallow 2400 psi Equate Mmax and Mallow and solve for w: tallow 100 psi 89 wb 12 2 Find wallow (lb/ft ) (a) ALLOWABLE LOAD BASED UPON BENDING STRESS IN THE (b) ALLOWABLE ; LOAD BASED UPON SHEAR STRESS IN THE PLANKS PLANKS Let b 121 lb/ft2 900 b w1 See the free-body diagram in part (a). width of one plank (in.) A 1.5b (in.2) Vmax occurs at the inside face of the support. S b (1.5 in.)2 6 Vmax qa 89 in. b 2 (44.5) a 0.375b (in.3) Free-body diagram of one plank supported on the beams: (V 44.5q wb b 144 89 wb 288 lb/ft2; b lb; w in.) Allowable shear force: t 3V 2A Vallow 2Atallow 3 2(1.5 b)(100 psi) 3 100 b (lb) Equate Vmax and Vallow and solve for w: 89wb 288 100b w2 324 lb/ft2 ; (c) ALLOWABLE LOAD Bending stress governs. wallow 121 lb/ft2 ; ...
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