457_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

457_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ; ...
View Full Document

Ask a homework question - tutors are online