912_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

912_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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906 CHAPTER 11 Columns Solution 11.9-27 Aluminum bar Alloy 6061-T6 Pinned supports (a) F IND L max IF d 1.0 in. Assume L/r is less than 66: Solve For L max (59.29) r 14.8 in. ; L / r : L r 59.29 L r 6 66 ok or 12.73 20.2 0.126 ( L / r ) Eq.(11-85 a ): s allow 20.2 0.126 ( L / r ) ksi s allow P A 10 k 0.7854 in. 2 12.73 ksi r A I A d 4 0.2500 in. A p d 2 4 0.7854 in. 2 I p d 4 64 ( K 1). P 10 k (b) F IND d min IF Assume L/r is greater than 66: Eq. (11-85 b ): L / r 80/ d 80/1.12 71 7 66 ok d 4 1.597 in. 4 d min 1.12 in. ; or 12.73 d 2 51,000 (80/ d ) 2 s allow 51,000 ksi ( L / r ) 2 s allow P A 10 k p d 2 /4 12.73 d 2 (ksi) A p d 2 4 r d 4 L r 20 in. d /4 80 in. d L 20 in. Assume L/r is less than 55: Eq. (11-84 a ): Solve for (b) F IND d min IF s allow P A 39.34 k p d 2 /4 50.09 d 2 (ksi) A p d 2 4 r d 4 L r 23.62 in. d /4 94.48 in. d L 0.6 m 23.62 in. L max (45.65) r 17.98 in. 457 mm ; L / r : L r 45.65 L r 6 55 ok or 20.20 30.7 0.23 ( L / r ) s allow 30.7 0.23 ( L / r ) ksi Assume L/r is greater than 55:
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