Question

An aluminum alloy tube with an outside diameter of 3.50 in. and a wall thickness of 0.30 in. is used as a 14 ft long column. Assume that E = 10,000 ksi and that pinned connections are used at each end of the column. Determine the slenderness ratio and the Euler buckling load for the column.

Answer 1

slenderness ratio = 147.8

buckling load = 13.62 kips

Step-by-step explanation:

Given data:

outside diameter is 3.50 inc

wall thickness 0.30 inc

length of column is 14 ft

E = 10,000 ksi

moment of inertia
`= (\pi)/(64 (D_O^2 -D_i^2))`

`I = (\pi)/(64)(3.5^2 -2.9^2) = 3.894 in^4`

Area
`= (\pi)/(4) (3.5^2 -2.9^2) = 3.015 in^2`

`radius = \sqrt{(I)/(A)}`

`r = \sqrt{(3.894)/(3.015)`

r = 1.136 in

slenderness ratio
`= (L)/(r)`

`= (14 *12)/(1.136) = 147.8`

buckling load
`= P_cr = \frac{\pi^2 EI}}{l^2}`

`P_(cr) = (\pi^2 *10,000*3.844)/(( 14* 12)^2)`

`P_(cr) = 13.62 kips`