LECTURE+39+COE-3001-A

Is pcr for these other 3 cases pcr

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Unformatted text preview: th of the equivalent pinned- end column 4/17/13 M. Mello/Georgia Tech Aerospace EXAMPLE 9- 2 GIVEN: A viewing planorm is supported by a row of Aluminum pipe columns having length L = 3.25m and outside diameter d = 100 mm. The columns are designed to support compressive loads of P=100kN. Also E= 72GPa and σpl = 480MPa. DETERMINE: Minimum required thickness (t) of the columns if a safety factor of n=3 is required with respect to Euler buckling. SOLUTION: Model each column as a fixed- pinned column Pcr 4/17/13 2.046⇡ 2 EI = L2 ⇡⇥ 2 A= d (d 4 A = 1999mm2 ☜ Case (d) in table of previous slide M. Mello/Georgia Tech Aerospace 2t) 2 ⇤ EXAMPLE 9- 2 ⇡⇥ ⇤ ☞ moment of iner>a: I = d4 d4 i 64 o ⇤ ⇡⇥ 4 I= d ( d 2 t) 4 64 ⇡⇥ I= (0.1m)4 (0.1m 64 ☞ Invoke safety factor: Pcr = nPallow 2t)4 ⇤ Pcr = 3(100kN ) = 300kN 2.046⇡ 2 EI = 2 and solve for thickness (t). L ☞ Now subs>tute into Pcr t = 0.006825m = 6.83mm ☜ ANSWER ☞ Check cri>cal stress in column against propor>onal limit σpl = 480MPa cr = 4/17/13 Pcr A cr = 300kN 1999mm2 cr = 150M P a M. Mello/Georgia Tech Aerospace () cr < pl )...
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