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 t max and t min in the webs of the beam due to a shear force V 5 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 5 28 k 5 28,000 lb t 1 5 1.0 in. b 5 12 in. b 1 5 10 in. t 5 2 t 1 5 2.0 in. M OMENT OF INERTIA M AXIMUM SHEAR STRESS IN THE WEB ( AT NEUTRAL AXIS ) y 1 5 1 2 ¢ b 2 5 b 4 Ê y 2 5 1 2 ¢ b 1 2 5 b 1 4 A 2 5 b 1 ¢ b 1 2 5 b 2 1 2 A 1 5 b ¢ b 2 5 b 2 2 Q 5 A 1 y 1 2 A 2 y 2 I 5 1 12 ( b 4 2 b 4 1 ) 5 894.67 in. 4 t 5 VQ It 5 1.42 ksi M INIMUM SHEAR STRESS IN THE WEB ( AT LEVEL A-A ) 5 1.03 ksi t min 5 VQ It 5 (28,000 lb)(66.0 in. 3 ) (894.67 in. 4 )(2.0 in.) 5 1033 psi Q 5 (12 in.) 8 [(12 in.) 2 2 (10 in.) 2 ] 5 66.0 in. 3 t 1 5 b 2 b 1 2 Ê Q 5 b 8 ( b 2 2 b 1 2 ) Q 5 Ay 5 ( bt 1 ) ¢ b 2 2 t 1 2 5 bt 1 2 ( b 2 t 1 ) t max 5 VQ It 5 (28,000 lb)(91.0 in.
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