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05-04ChapGere.0011

# 05-04ChapGere.0011 - 348 A-PDF Stresses in Beams(Basic...

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Problem 5.10-11 A hollow aluminum box beam has the square cross section shown in the figure. Calculate the maximum and minimum shear stresses max and min in the webs of the beam due to a shear force V 28 k. Solution 5.10-11 Square box beam 348 CHAPTER 5 Stresses in Beams (Basic Topics) 1.0 in. 1.0 in. 12 in. V 28 k 28,000 lb t 1 1.0 in. b 12 in. b 1 10 in. t 2 t 1 2.0 in. M OMENT OF INERTIA M AXIMUM SHEAR STRESS IN THE WEB ( AT NEUTRAL AXIS ) y 1 1 2 ¢ b 2 b 4 y 2 1 2 ¢ b 1 2 b 1 4 A 2 b 1 ¢ b 1 2 b 2 1 2 A 1 b ¢ b 2 b 2 2 Q A 1 y 1 A 2 y 2 I 1 12 ( b 4 b 4 1 ) 894.67 in. 4 t VQ It 1.42 ksi M INIMUM SHEAR STRESS IN THE WEB ( AT LEVEL A-A ) 1.03 ksi t min VQ It (28,000 lb)(66.0 in. 3 ) (894.67 in. 4 )(2.0 in.) 1033 psi Q (12 in.) 8 [ (12 in.) 2 (10 in.) 2 ] 66.0 in. 3 t 1 b b 1 2 Q b 8 ( b 2 b 1 2 ) Q Ay ( bt 1 ) ¢ b 2 t 1 2 bt 1 2 ( b t 1
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