05-04ChapGere.0012

05-04ChapGere.0012 - ALL DIMENSIONS IN INCHES M OMENT OF...

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Solution 5.10-12 T-beam SECTION 5.10 Shear Stresses in the Webs of Beams with Flanges 349 b 5 220 mm t 5 15 mm h 5 300 mm h 1 5 275 mm V 5 60 kN Find t max L OCATE NEUTRAL AXIS ( ALL DIMENSIONS IN MILLIMETERS ) 5 (220)(25) ¢ 25 2 1 (15)(275) ¢ 300 2 275 2 (220)(25) 1 (15)(275) 5 76.79 mm c 5 g Ay g A 5 b ( h 2 h 1 ) ¢ h 2 h 1 2 1 th 1 ¢ h 2 h 1 2 b ( h 2 h 1 ) 1 th 1 M OMENT OF INERTIA ABOUT THE z- AXIS 5 56.29 3 10 6 mm 4 5 23.02 3 10 6 mm 4 I 5 I web 1 I flange 5 79.31 3 10 6 mm 4 F IRST MOMENT OF AREA ABOVE THE z AXIS 5 373.6 3 10 3 mm 3 M AXIMUM SHEAR STRESS 5 18.8 MPa t max 5 VQ It 5 (60 kN)(373.6 3 10 3 mm 3 ) (79.31 3 10 6 mm 4 )(15 mm) Q 5 (15)(223.2) ¢ 223.2 2 I flange 5 1 12 (220)(25) 3 1 (220)(25) ¢ 76.79 2 25 2 2 I web 5 1 3 (15)(223.2) 3 1 1 3 (15)(76.79 2 25) 3 z y C 275 1.5 220 223.2 76.79 25 Problem 5.10-13 Calculate the maximum shear stress t max in the web of the T-beam shown in the figure if b 5 10 in., t 5 0.6 in., h 5 8 in., h 1 5 7 in., and the shear force V 5 5000 lb. Solution 5.10-13 T-beam b 5 10 in. t 5 0.6 in. h 5 8 in. h 1 5 7 in. V 5 5000 lb Find t max L OCATE NEUTRAL AXIS
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Unformatted text preview: ( ALL DIMENSIONS IN INCHES ) M OMENT OF INERTIA ABOUT THE z-AXIS 5 50.48 in. 4 I web 5 1 3 (0.6)(6.317) 3 1 1 3 (0.6)(1.683 2 1.0) 3 5 (10)(1)(0.5) 1 (0.6)(7)(4.5) 10(1) 1 (0.6)(7) 5 1.683 in. c 5 g Ay g A 5 b ( h 2 h 1 ) ¢ h 2 h 1 2 ≤ 1 th 1 ¢ h 2 h 1 2 ≤ b ( h 2 h 1 ) 1 th 1 5 14.83 in. 4 I 5 I web 1 I flange 5 65.31 in 4 . F IRST MOMENT OF AREA ABOVE THE z AXIS M AXIMUM SHEAR STRESS t max 5 VQ It 5 (5000 lb)(11.97 in. 3 ) (65.31 in. 4 )(0.6 in.) 5 1530 psi Q 5 (0.6)(6.317) ¢ 6.317 2 ≤ 5 11.97 in. 3 I flange 5 1 12 (10)(1.0) 3 1 (10)(1.0)(1.683 2 0.5) 2 z y C h 1 h c t b z y C 7 1.683 0.6 10 6.317 1.0 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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