916_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

916_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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910 CHAPTER 11 Columns Solution 11.9-33 Wood column (square cross section) (a) M AXIMUM LENGTH L max FOR b ± d ± 5.5 in. From Eq. (11-92): From Eq. (11-95): Trial and error: From Eq. (11-94): ± 75.2 in. L max ± 13.67 d ± (13.67)(5.5 in.) L d ± A K cE E f F c ± 13.67 f ± 1.3225 C P ± 0.77783 ± 1 + f 1.6 ² A c 1 + f 1.6 d 2 ² f 0.8 C P ± P F C b 2 ± 0.77783 K cE ± 0.3 P ± 40 k F c ± 1,700 psi E ± 1,400,000 psi c ± 0.8 (b) M INIMUM DIMENSION b min for L ± 11 ft Trial and error: Given load: P ± 40 k P ± F c C P b 2 C P ± 1 + f 1.6 ² A c 1 + f 1.6 d 2 ² f 0.8 f ± K cE E F c ( L / d ) 2 L d ± L b Trial (in.) (kips) 6.50 20.308 0.59907 0.49942 35.87 6.70 19.701 0.63651 0.52230 39.86 6.71 19.672 0.63841 0.52343 40.06 b min ± 6.71 in. ; P C P f L d ± L b b Problem 11.9-34 A square wood column with side dimensions b (see figure) is constructed of a structural grade of southern pine for which F c ± 10.5 MPa and E ± 12 GPa. An axial force P ± 200 kN acts on the column.
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Unformatted text preview: (a) If the dimension b ± 150 mm, what is the maximum allowable length L max of the column? (b) If the length L ± 4.0 m, what is the minimum required dimension b min ? Solution 11.9-34 Wood column(square cross section) (a) M AXIMUN LENGTH FOR From Eq. (11-92): From Eq. (11-95): C P ± 0.84656 ± 1 + f 1.6 ² A c 1 + f 1.6 d 2 ² f 0.8 C P ± P F c b 2 ± 0.84656 150 mm b ± d ± L max K cE ± 0.3 P ± 200 kN F c ± 10.5 MPa E ± 12 GPa c ± 0.8 Trial and error: From Eq. (11-94): ± 2.08 m ; ‹ L max ± 13.876 d ± (13.876)(150 mm) L d ± A K cE E f F c ± 13.876 f ± 1.7807 11Ch11.qxd 9/27/08 2:27 PM Page 910...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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