05-03ChapGere.0016

# 05-03ChapGere.0016 - V max occurs at the inside face of the...

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Problem 5.8-12 A wood beam ABC with simple supports at A and B and an overhang BC has height h 280 mm (see figure). The length of the main span of the beam is L 3.6 m and the length of the overhang is L /3 1.2 m. The beam supports a concentrated load 3 P 15 kN at the midpoint of the main span and a load P 5 kN at the free end of the overhang. The wood has weight density 5.5 kN/m 3 . (a) Determine the required width b of the beam based upon an allowable bending stress of 8.2 MPa. (b) Determine the required width based upon an allowable shear stress of 0.7 MPa. Solution 5.8-12 Rectangular beam with an overhang 336 CHAPTER 5 Stresses in Beams (Basic Topics) (b) A LLOWABLE LOAD BASED UPON SHEAR STRESS IN THE PLANKS See the free-body diagram in part (a).
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Unformatted text preview: V max occurs at the inside face of the support. ( V 5 lb; w 5 lb/ft 2 ; b 5 in.) Allowable shear force: t 5 3 V 2 A Ê V allow 5 2 A t allow 3 5 2(1.5 b )(100 psi) 3 5 100 b (lb) V max 5 q ¢ 89 in. 2 ≤ 5 44.5 q 5 (44.5) ¢ wb 144 ≤ 5 89 wb 288 E QUATE V max AND V allow AND SOLVE FOR w: w 2 5 324 lb/ft 2 (c) A LLOWABLE LOAD Bending stress governs. w allow 5 121 lb/ft 2 89 wb 288 5 100 b A C B P b h = 280 mm 3 P L L 2 — L 3 — A C B P b h = 280 mm 3 P L 3 — L 2 — L 2 — q R A R B P R A V qL 18 7 P 6 ] qL 3 P 1 qL 18 ] 11 P 6 ] 5qL 9 ] 11 P 6 ] L 5 3.6 m P 5 5 kN g 5 5.5 kN/m 3 (for the wood) q 5 g bh A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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