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05-05ChapGere.0005

05-05ChapGere.0005 - as a reference axis 5(200(50(100...

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Solution 5.11-7 Wood beam with plywood webs 354 CHAPTER 5 Stresses in Beams All dimensions in inches. b 5 3.375 b 1 5 3.0 h 5 8.0 h 1 5 6.5 F 5 allowable shear force for one nail 5 30 lb s 5 longitudinal spacing of the nails f 5 shear flow between one flange and both webs Q 5 Q flange 5 A f d f 5 (3.0)(0.75)(3.625) 5 8.1563 in. 3 I 5 1 12 ( bh 3 2 b 1 h 1 3 ) 5 75.3438 in. 4 s max 5 2 FI VQ f 5 VQ I 5 2 F s (a) V 5 200 lb 5 2.77 in. (b) V 5 300 lb By proportion, s max 5 (2.77 in.) ¢ 200 300 5 1.85 in. s max 5 2 FI VQ 5 2(30 lb)(75.344 in. 4 ) (200 lb)(8.1563 in. 3 ) Problem 5.11-8 A beam of T cross section is formed by nailing together two boards having the dimensions shown in the figure. If the total shear force V acting on the cross section is 1600 N and each nail may carry 750 N in shear, what is the maximum allowable nail spacing s ? Solution 5.11-8 T-beam (nailed) z y C 50 mm 50 mm 200 mm 200 mm z y C t t b h 1 h B B c 1 c 2 All dimensions in millimeters. V 5 1600 N F 5 allowable load per nail F 5 750 N b 5 200 mm t 5 50 mm h 5 250 mm h 1 5 200 mm s 5 nail spacing Find s max L OCATION OF NEUTRAL AXIS ( z AXIS ) Use the lower edge of the cross section (line B-B)
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Unformatted text preview: as a reference axis. 5 (200)(50)(100) 1 (200)(50)(225) 5 3.25 3 10 6 mm 3 Q BB 5 ( h 1 t ) ¢ h 1 2 ≤ 1 ( bt ) ¢ h 2 t 2 ≤ A 5 bt 1 h 1 t 5 t ( b 1 h 1 ) 5 (50)(400) 5 20 3 10 3 mm 2 c 1 5 h 2 c 2 5 250 2 162.5 5 87.5 mm M OMENT OF INERTIA ABOUT THE NEUTRAL AXIS 5 113.541 3 10 6 mm 4 F IRST MOMENT OF AREA OF FLANGE M AXIMUM ALLOWABLE SPACING OF NAILS 5 85.2 mm s max 5 F allow I VQ 5 (750 N)(113.541 3 10 6 mm 4 ) (1600 N)(625 3 10 3 mm 3 ) f 5 VQ I 5 F s Q 5 bt ¢ c 1 2 t 2 ≤ 5 (200)(50)(62.5) 5 625 3 10 3 mm 3 1 (200)(50)(62.5) 2 5 1 3 (50)(162.5) 3 1 1 3 (50)(37.5) 3 1 1 12 (200)(50) 3 I 5 1 3 tc 2 3 1 1 3 t ( h 1 2 c 2 ) 3 1 1 12 bt 3 1 bt ¢ c 1 2 t 2 ≤ 2 c 2 5 Q BB A 5 3.25 3 10 6 mm 3 20 3 10 3 mm 2 5 162.5 mm A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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