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05-01ChapGere.0011

# 05-01ChapGere.0011 - S UBSTITUTE NUMERICAL VALUES s max 5...

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Problem 5.5-12 A small dam of height h 5 2.0 m is constructed of vertical wood beams AB of thickness t 5 120 mm, as shown in the figure. Consider the beams to be simply supported at the top and bottom. Determine the maximum bending stress s max in the beams, assuming that the weight density of water is ± 5 9.81 kN/m 3 . Solution 5.5-12 Vertical wood beam SECTION 5.5 Normal Stresses in Beams 295 h t A B h 5 2.0 m t 5 120 mm ± 5 9.81 kN/m 3 (water) Let b 5 width of beam perpendicular to the plane of the figure Let q 0 5 maximum intensity of distributed load q 0 5 g bh Ê S 5 bt 2 6 M AXIMUM BENDING MOMENT Substitute into the equation for M: For the vertical wood beam: Maximum bending stress
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Unformatted text preview: S UBSTITUTE NUMERICAL VALUES : s max 5 2.10 MPa N OTE : For b 5 1.0 m, we obtain q 5 19,620 N/m, S 5 0.0024 m 3 , M max 5 5,034.5 N ? m, and s max 5 M max / S 5 2.10 MPa s max 5 M max S 5 2 q h 2 3 Ï 3 bt 2 5 2 g h 3 3 Ï 3 t 2 L 5 h ; M max 5 q h 2 9 Ï 3 M max 5 q L 6 ¢ L Ï 3 ≤ 2 q 6 L ¢ L 3 3 Ï 3 ≤ 5 q L 2 9 Ï 3 x 5 L / Ï 3 dM dx 5 q L 6 2 q x 2 2 L 5 Ê x 5 L Ï 3 5 q Lx 6 2 q x 3 6 L M 5 R A x 2 q x 3 6 L R A 5 q L 6 h A B q t L A B q R A x ( ] ) x q 5 q 0 L A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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