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911_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

911_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Problem 11.9-25 A solid round bar of aluminum having diameter d (see figure) is compressed by an axial force P 60 k. The bar has pinned supports and is made of alloy 2014-T6. (a) If the diameter d 2.0 in., what is the maximum allowable length L max of the bar? (b) If the length L 30 in., what is the minimum required diameter d min ? SECTION 11.9 Aluminum Columns 905 Solution 11.9-25 Aluminum bar Alloy 2014-T6 Pinned ends (a) F IND L max IF d 2.0 in. Assume L/r is less than 55: Eq. (11-84 a ): L max (50.43) r 25.2 in. ; Solve for L / r : L r 50.43 L r 6 55 ok or 19.10 30.7 0.23( L / r ) s allow 30.7 0.23( L / r ) ksi s allow P A 60 k 3.142 in. 2 19.10 ksi r A I A d 4 0.5 in. A p d 2 4 3.142 in. 2 I p d 4 64 ( K 1). P 60 k (b) F IND d min IF L 30 in. Assume L/r is greater than 55: L / r 120/ d 120/2.12 56.6 7 55 ok d 4 20.37 in. 4 d min 2.12 in. ; or 76.39 d 2 54,000 (120/ d ) 2 Eq.(11-84 b ): s allow 54,000 ksi ( L / r ) 2 s allow P A 60 k p d 2 /4 76.39 d 2 (ksi) A p d 2 4 r d r L r 30 in. d /4 120 in. d Problem 11.9-26 A solid round bar of aluminum having diameter
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Unformatted text preview: d (see figure) is compressed by an axial force P ± 175 kN. The bar has pinned supports and is made of alloy 2014-T6. (a) If the diameter d ± 40 mm, what is the maximum allowable length L max of the bar? (b) If the length L ± 0.6 m, what is the minimum required diameter d min ? ( Hint: Convert the given data to USCS units, determine the required quantities, and then convert back to SI units.) d Probs. 11.9-25 through 11.9-28 Solution 11.9-26 Aluminum bar Alloy 2014-T6 Pinned supports (a) F IND L max IF d ± 40 mm ± 1.575 in. A ± p d 2 4 ± 1.948 in. 2 I ± p d 4 64 ( K ± 1). P ± 175 kN ± 39.34 k s allow ± P A ± 39.34 k 1.948 in. 2 ± 20.20 ksi r ± A I A ± d 4 ± 0.3938 in. 11Ch11.qxd 9/27/08 2:27 PM Page 905...
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