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477_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 477_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 5.11 Built-Up Beams 471 Solution 5.11-7 Wood beam with plywood webs All dimensions in inches. allowable shear force for one nail longitudinal spacing of the nails shear flow between one flange and both webs Q Q flange A f d f (3.0)(0.75)(3.625) 8.1563 in. 3 I 1 12 ( bh 3 b 1 h 1 3 ) 75.3438 in. 4 f VQ I 2 F s s max 2 FI VQ f s 30 lb F h 8.0 h 1 6.5 b 3.375 b 1 3.0 (a) (b) By proportion, s max (2.77 in.) a 200 300 b 1.85 in. ; V 300 lb 2.77 in. ; s max 2 FI VQ 2(30 lb)(75.344 in. 4 ) (200 lb)(8.1563 in. 3 ) V 200 lb 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 acting on the cross section is 1500 N and each nail may carry 760 N in shear, what is the maximum allowable nail spacing
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Unformatted text preview: s V z y C 60 mm 60 mm 240 mm 200 mm Solution 5.11-8 L OCATION OF NEUTRAL AXIS ( AXIS ) c 1 ± 89.091 mm c 1 ± h ² c 2 c 2 ± 170.909 mm c 2 ± bt a h 1 ³ t 2 b + th 1 h 1 2 A z A ± bt + h 1 t A ± 2.64 * 10 4 mm 2 h ± 260 mm t ± 60 mm b ± 240 mm h 1 ± 200 mm V ± 1500 N F allow ± 760 N M OMENT OF INERTIA ABOUT THE NEUTRAL AXIS F IRST MOMENT OF AREA OF FLANGE M AXIMUM ALLOWABLE SPACING OF NAILS ; s max ± F allow I VQ s max ± 92.3 mm f ± VQ I ± F s Q ± 8.509 * 10 5 mm 3 Q ± bt a c 1 ² t 2 b I ± 1.549 * 10 8 mm 4 + 1 12 bt 3 + bt a c 1 ² t 2 b 2 I ± 1 3 tc 2 3 + 1 3 t 1 h 1 ² c 2 2 3 05Ch05.qxd 9/25/08 2:29 PM Page 471...
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