428_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

428_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 05Ch05.qxd 9/24/08 422 4:59 AM Page 422 CHAPTER 5 Stresses in Beams (Basic Topics) qallow qallow sa S 12 in./ft 2.5 a2 lb 1055 ft MZ 8.00E+00 w ; for moment release (b) SHEAR RELEASE AT C-GIVES MAX. MOMENT AT C (SEE MOMENT DIAGRAM) 8 q a2 qallow sa S 12 in./ft 8a2 qallow lb ft ; for shear release w Problem 5.6-14 A small balcony constructed of wood is supported by three identical cantilever beams (see figure). Each beam has length L1 2.1 m, width b, and height h 4b/3. The dimensions of the balcon floor are L1 * L2, with L2 2.5 m. The design load is 5.5 kPa acting over the entire floor area. (This load accounts for all loads except the weights of the cantilever beams, which have a weight density g 5.5 kN/m3.) The allowable bending stress in the cantilevers is 15 MPa. Assuming that the middle cantilever supports 50% of the load and each outer cantilever supports 25% of the load, determine the required dimensions b and h. Solution 5.6-14 282 4b h= — 3 L2 b L1 Compound beam MAXIMUM BENDING MOMENT (q q0)L2 1 1 (6875 N/m Mmax 2 2 7333b2)(2.1 m)2 15,159 + 16,170b2 (N # m) bh2 6 8b3 27 sallow S L1 2.1 m L2 2.5 m Floor dimensions: L1 * L2 Design load w 5.5 kPa g 5.5 kN/m3 (weight density of wood beam) sallow 15 MPa S MIDDLE BEAM SUPPORTS 50% OF THE LOAD. Rearrange the equation: ‹q wa L2 b 2 (5.5 kPA) a 2.5 m b 2 WEIGHT OF BEAM q0 gbh 4gb2 3 7333b2 (N/m) 4 (5.5 kN/m2) b2 3 (b meters) 6875 N/m Mmax 15,159 + 16,170b2 (120 * 106)b3 (15 * 106 N/m2) a 436,590b2 409,300 SOLVE NUMERICALLY FOR DIMENSION b 4b 0.2023 m h b 0.1517 m 3 REQUIRED DIMENSIONS b 152 mm h 202 mm ; 8b3 b 27 0 ...
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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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