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909_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

909_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Aluminum Columns Problem 11.9-21 An aluminum pipe column (alloy 2014-T6) with pinned ends has outside diameter d 2 5.60 in. and inside diameter d 1 4.80 in. (see figure). Determine the allowable axial load P allow for each of the following lengths: L 6 ft, 8 ft, 10 ft, and 12 ft. Probs. 11.9-21 through 11.9-24 SECTION 11.9 Aluminum Columns 903 Solution 11.9-21 Aluminum pipe column Alloy 2014-T6 Pinned ends . 1.844 in. r A I A I p 4 ( d 2 4 d 1 4 ) 22.22 in. 4 A p 4 ( d 2 2 d 1 2 ) 6.535 in. 2 d 1 4.80 in. d 2 5.60 in. ( K 1) Use Eqs. (11-84 a and b ): s allow 54,000/( L / r ) 2 ksi L / r Ú 55 s allow 30.7 0.23 ( L / r ) ksi L / r 55 L (ft) 6 ft 8 ft 10 ft 12 ft L/r 39.05 52.06 65.08 78.09 s allow (ksi) 21.72 18.73 12.75 8.86 P allow s allow A 142 k 122 k 83 k 58 k d 1 d 2 Problem 11.9-22 An aluminum pipe column (alloy 2014-T6) with pinned ends has outside diameter and inside diameter (see figure). Determine the allowable axial load P allow for each of the following lengths: L 1.0 m, 2.0 m, 3.0 m , and 4.0 m.
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Unformatted text preview: ( Hint : Convert the given data to USCS units, determine the required quantities, and then convert back to SI units.) d 1 ± 110 mm d 2 ± 120 mm Solution 11.9-22 Aluminum pipe column Alloy 2014-T6 Pinned ends . r ± A I A ± 40.697 mm ± 1.6022 in. I ± p 64 ( d 2 4 ² d 1 4 ) ± 7.188 in. 4 A ± p 4 ( d 2 2 ² d 1 2 ) ± 2.800 in. 2 d 1 ± 110 mm ± 4.3307 in. d 2 ± 120 mm ± 4.7244 in. ( K ± 1) Use Eqs. (11-84 a and b ): s allow ± 54,000/( L / r ) 2 ksi L / r Ú 55 s allow ± 30.7 ² 0.23 ( L / r ) ksi L / r … 55 L (m) 1.0 m 2.0 m 3.0 ft 4.0 m L (in.) 39.37 78.74 118.1 157.5 L/r 24.58 49.15 73.73 98.30 s allow (ksi) 25.05 19.40 9.934 5.588 P allow ± s allow A 70.14 k 54.31 k 27.81 k 15.65 k P allow (kN) 312 kN 242 kN 124 kN 70 kN 11Ch11.qxd 9/27/08 2:27 PM Page 903...
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