406_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

406_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 400 4:59 AM Page 400 CHAPTER 5 Stresses in Beams (Basic Topics) Problem 5.5-12 A small dam of height h 2.0 m is constructed of vertical wood beams AB of thickness t 120 mm, as shown in the figure. Consider the beams to be simply supported at the top and bottom. Determine the maximum bending stress smax in the beams, assuming that the weight density of water is g 9.81 kN.m3 A h t B Solution 5.5-12 Vertical wood beam MAXIMUM BENDING MOMENT RA M h 120 mm g 9.81kN/ m3(water) RAx 2.0 m t q0L 6 dM dx q0 x 3 6L q0 Lx q0 x 3 6 6L q0L q0x 2 0x 6 2L Substitute x Let q0 = maximum intensity of distributed load Mmax q0 gbh S bt2 6 L/ 13 into the equation for M: q0L L a b 6 13 Let b = width of beam perpendicular to the plane of the figure L 13 q0 L3 a b 6L 3 13 For the vertical wood beam: L 3 13 bt2 Maximum bending stress smax Mmax S 2q0 h2 9 13 q0 L2 h; Mmax 3 13 t2 9 13 q0 h 2 2gh3 SUBSTITUTE NUMERICAL VALUES: smax 2.10 MPa ; NOTE: For b 1.0 m, we obtain q0 19,620 N/m, S 0.0024 m3, Mmax 5,034.5 N # m, and smax Mmax/S 2.10 MPa ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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